Quantum secret sharing（QSS） is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2k- 1, 1, k] quantum error-correcting code （QECC） to im...Quantum secret sharing（QSS） is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2k- 1, 1, k] quantum error-correcting code （QECC） to implement a quantum （k, 2k-1） threshold scheme. It also takes advantage of classical enhancement of the [2k-1, 1, k] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously. Because information is encoded into QECC, these schemes can prevent intercept-resend attacks and be implemented on some noisy channels.展开更多
Linear dispersion codes (LDCs) were originally designed based on maximum likelihood detection. They do not have good performance when using ordered successive interference cancellation (OSIC) detection. In this paper,...Linear dispersion codes (LDCs) were originally designed based on maximum likelihood detection. They do not have good performance when using ordered successive interference cancellation (OSIC) detection. In this paper,we propose a new improved linear dispersion codes transmission scheme to combat performance loss of original LDCs when using OSIC detection. We introduce an interleaver to each data substream transmitted over different antennas after LDCs encoder. Furthermore,a new computer search criterion for a linear transformation matrix is also proposed. New search criterion is to minimize the symbol error rate based on OSIC detection. Computer simulations show that the performance of proposed LDCs transmission scheme is better than the original LDCs.展开更多
This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block co...This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block code share the propertyof linear correlation, the existing linear correlation-basedidentification method is invalid for this case. This drawback can becircumvented by introducing a novel multi-fractal spectrum-basedmethod. Simulation results show that the new method has highrobustness and under the same conditions of bit error, the lowerthe code rate, the higher the recognition rate. Thus, the methodhas significant potential for future application in engineering.展开更多
Stereolithographic(STL)files have been extensively used in rapid prototyping industries as well as many other fields as watermarking algorithms to secure intellectual property and protect three-dimensional models from...Stereolithographic(STL)files have been extensively used in rapid prototyping industries as well as many other fields as watermarking algorithms to secure intellectual property and protect three-dimensional models from theft.However,to the best of our knowledge,few studies have looked at how watermarking can resist attacks that involve vertex-reordering.Here,we present a lossless and robust watermarking scheme for STL files to protect against vertexreordering attacks.Specifically,we designed a novel error-correcting code(ECC)that can correct the error of any one-bit in a bitstream by inserting several check digits.In addition,ECC is designed to make use of redundant information according to the characteristics of STL files,which introduces further robustness for defense against attacks.No modifications are made to the geometric information of the three-dimensional model,which respects the requirements of a highprecision model.The experimental results show that the proposed watermarking scheme can survive numerous kinds of attack,including rotation,scaling and translation(RST),facet reordering,and vertex-reordering attacks.展开更多
In this paper,we first generalize the constant dimension and orbit codes over finite fields to the constant rank and orbit codes over finite chain rings.Then we provide a relationship between constant rank codes over ...In this paper,we first generalize the constant dimension and orbit codes over finite fields to the constant rank and orbit codes over finite chain rings.Then we provide a relationship between constant rank codes over finite chain rings and constant dimension codes over the residue fields.In particular,we prove that an orbit submodule code over a finite chain ring is a constant rank code.Finally,for special finite chain ring F_(q)+γF_(q),we define a Gray mapφfrom(F_(q)+γF_(q))^(n)to F^(2n)_(q),and by using cyclic codes over F_(q)+γF_(q),we obtain a method of constructing an optimum distance constant dimension code over F_(q).展开更多
In this work, the homomorphism of the classic linear block code in linear network coding for the case of binary field and its extensions is studied. It is proved that the classic linear error-control block code is hom...In this work, the homomorphism of the classic linear block code in linear network coding for the case of binary field and its extensions is studied. It is proved that the classic linear error-control block code is homomorphic network error-control code in network coding. That is, if the source packets at the source node for a linear network coding are precoded using a linear block code, then every packet flowing in the network regarding to the source satisfies the same constraints as the source. As a consequence, error detection and correction can be performed at every intermediate nodes of multicast flow, rather than only at the destination node in the conventional way, which can help to identify and correct errors timely at the error-corrupted link and save the cost of forwarding error-corrupted data to the destination node when the intermediate nodes are ignorant of the errors. In addition, three examples are demonstrated which show that homomorphic linear code can be combined with homomorphic signature, McEliece public-key cryptosystem and unequal error protection respectively and thus have a great potential of practical utility.展开更多
Abraham Lempel et al made a connection between linear codes and systems of bilinear forms over finite fields. In this correspondence, a new simple proof of a theorem in [1] is presented; in addition, the encoding proc...Abraham Lempel et al made a connection between linear codes and systems of bilinear forms over finite fields. In this correspondence, a new simple proof of a theorem in [1] is presented; in addition, the encoding process and the decoding procedure of RS codes are simplified via circulant matrices. Finally, the results show that the correspondence between bilinear forms and linear codes is not unique.展开更多
Let F_qbe afinite field with q=pmelements,where pis an odd prime and mis apositive integer.Here,let D_0={(x_1,x_2)∈F_q^2\{(0,0)}:Tr(x_1^(pk1+1)+x_2^(pk2+1))=c},where c∈F_q,Tr is the trace function fromFF_qtoFpand m/...Let F_qbe afinite field with q=pmelements,where pis an odd prime and mis apositive integer.Here,let D_0={(x_1,x_2)∈F_q^2\{(0,0)}:Tr(x_1^(pk1+1)+x_2^(pk2+1))=c},where c∈F_q,Tr is the trace function fromFF_qtoFpand m/(m,k_1)is odd,m/(m,k_2)is even.Define ap-ary linear code C_D =c(a_1,a_2):(a_1,a_2)∈F_q^2},where c(a_1,a_2)=(Tr(a_1x_1+a_2x_2))_((x1,x2)∈D).At most three-weight distributions of two classes of linear codes are settled.展开更多
The optimal and suboptimal structured algorithms of linear block codes from the geometrical perspective are represented.The minimum distance and weight property lemmas and the theorem are proved for the generator matr...The optimal and suboptimal structured algorithms of linear block codes from the geometrical perspective are represented.The minimum distance and weight property lemmas and the theorem are proved for the generator matrix.Based upon the property of generator matrix,the structured algorithms of linear block codes are demonstrated.Since the complexity of optimal structured algorithm is very high,the binary linear block codes is searched by using the suboptimal structured algorithm.The comparison with Bose-Chaudhuri-Hocquenqhem（BCH） codes shows that the searched linear block codes are equivalent on minimum distance and can be designed for more block lengths.Because the linear block codes are used widely in communication systems and digital applications,the optimal and suboptimal structured algorithms must have great future being widely used in many applications and perspectives.展开更多
The binary extended Golay code has a two-level structure, which can be used in the decoding of the code. However, such structure is not limited to the Golay code, in fact, several binary linear codes can be constructe...The binary extended Golay code has a two-level structure, which can be used in the decoding of the code. However, such structure is not limited to the Golay code, in fact, several binary linear codes can be constructed by a projective method which is related to the structure. In this correspondence, the binary (4n,n + 2k, ≥min(8, n,2d)) linear codes are resulted from quaternary (n,k,d) linear block codes. Based on the structure, the efficient maximum likelihood decoding algorithms can be presented correspondingly for the derived codes.展开更多
Firstly,the Fourier transforms in finite fields and the concept of linear complexityof sequences are described.Then several known lower bounds on the minimum distance of cycliccodes are outlined.Finally,the minimum di...Firstly,the Fourier transforms in finite fields and the concept of linear complexityof sequences are described.Then several known lower bounds on the minimum distance of cycliccodes are outlined.Finally,the minimum distance of cyclic codes is analyzed via linear complexityof sequences,and new theorems about the lower bounds are obtained.展开更多
A new architecture of space-time codes as a combination of orthogonal space-time block codes （OSTBC） and linear dispersion codes （LDC） is proposed in order to improve the bit error rate（BER） performance of OSTBC...A new architecture of space-time codes as a combination of orthogonal space-time block codes （OSTBC） and linear dispersion codes （LDC） is proposed in order to improve the bit error rate（BER） performance of OSTBC.The scheme proposed is named linear dispersion orthogonal space-time block codes （LDOSTBC）.In LDOSTBC scheme,firstly,the data is coded into LDC codewords.Then,the coded LDC substreams are coded into OSTBC codewords again.The decoding algorithm of LDOSTBC combines linear decoding of OSTBC and ML decoding or suboptimum detection algorithms of LDC.Compared with OSTBC scheme when the rate of LDC is MtR,the performance of LDOSTBC scheme can be improved without decreasing the data rate,where Mt is the number of transmit antennas and R is the spectral efficiency of the modulation constellation.If some rate penalty is allowed,when the rate of LDC is less than MtR the performance of LDOSTBC can be improved further.展开更多
In this paper, we propose a novel space efficient secret sharing scheme on the basis of minimal linear codes, which satisfies the definition of a computationally efficient secret sharing scheme. In the scheme, we part...In this paper, we propose a novel space efficient secret sharing scheme on the basis of minimal linear codes, which satisfies the definition of a computationally efficient secret sharing scheme. In the scheme, we partition the underlying minimal linear code into disjoint classes, establishing a one-to-one correspondence between the minimal authorized subsets of participants and the representative codewords of all different classes. Each participant, with only one short share transmitted through a public channel, can share a large secret. Therefore, the proposed scheme can distribute a large secret in practical applications such as secure information dispersal in sensor networks and secure multiparty computation.展开更多
This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theor...This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theory and the modern cryptography.展开更多
In this paper,we first give the definition of the Euclidean sums of linear codes,and prove that the Euclidean sums of linear codes are Euclidean dual-containing.Then we construct two new classes of optimal asymmetric ...In this paper,we first give the definition of the Euclidean sums of linear codes,and prove that the Euclidean sums of linear codes are Euclidean dual-containing.Then we construct two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of the Reed-Solomon codes,and two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of linear codes generated by Vandermonde matrices over finite fields.Moreover,these optimal asymmetric quantum errorcorrecting codes constructed in this paper are different from the ones in the literature.展开更多
m-weight,as a new generalization of classical Hamming weight,was discussedin this paper.A condition for the existence of linear codes of certain m-weights was given;theSingleton bound,Plotkin bound and Sphere Parking ...m-weight,as a new generalization of classical Hamming weight,was discussedin this paper.A condition for the existence of linear codes of certain m-weights was given;theSingleton bound,Plotkin bound and Sphere Parking bound of Hamming weight were correspondinglygeneralized to the m-weight.展开更多
Genetic algorithms offer very good performances for solving large optimization problems, especially in the domain of error-correcting codes. However, they have a major drawback related to the time complexity and memor...Genetic algorithms offer very good performances for solving large optimization problems, especially in the domain of error-correcting codes. However, they have a major drawback related to the time complexity and memory occupation when running on a uniprocessor computer. This paper proposes a parallel decoder for linear block codes, using parallel genetic algorithms (PGA). The good performance and time complexity are confirmed by theoretical study and by simulations on BCH(63,30,14) codes over both AWGN and flat Rayleigh fading channels. The simulation results show that the coding gain between parallel and single genetic algorithm is about 0.7 dB at BER = 10﹣5 with only 4 processors.展开更多
Deep holes are very important in the decoding of generalized RS codes, and deep holes of RS codes have been widely studied, but there are few works on constructing general linear codes based on deep holes. Therefore, ...Deep holes are very important in the decoding of generalized RS codes, and deep holes of RS codes have been widely studied, but there are few works on constructing general linear codes based on deep holes. Therefore, we consider constructing binary linear codes by combining deep holes with binary BCH codes. In this article, we consider the 2-error-correcting binary primitive BCH codes and the extended codes to construct new binary linear codes by combining them with deep holes, respectively. Furthermore, three classes of binary linear codes are constructed, and then we determine the parameters and the weight distributions of these new binary linear codes.展开更多
In this paper, error-correction coding (ECC) in Gray codes is considered and its performance in the protecting of spatial image watermarks against lossy data compression is demonstrated. For this purpose, the differen...In this paper, error-correction coding (ECC) in Gray codes is considered and its performance in the protecting of spatial image watermarks against lossy data compression is demonstrated. For this purpose, the differences between bit patterns of two Gray codewords are analyzed in detail. On the basis of the properties, a method for encoding watermark bits in the Gray codewords that represent signal levels by a single-error-correcting (SEC) code is developed, which is referred to as the Gray-ECC method in this paper. The two codewords of the SEC code corresponding to respective watermark bits are determined so as to minimize the expected amount of distortion caused by the watermark embedding. The stochastic analyses show that an error-correcting capacity of the Gray-ECC method is superior to that of the ECC in natural binary codes for changes in signal codewords. Experiments of the Gray-ECC method were conducted on 8-bit monochrome images to evaluate both the features of watermarked images and the performance of robustness for image distortion resulting from the JPEG DCT-baseline coding scheme. The results demonstrate that, compared with a conventional averaging-based method, the Gray-ECC method yields watermarked images with less amount of signal distortion and also makes the watermark comparably robust for lossy data compression.展开更多
Secret sharing is an important topic in cryptography and has applications in information security. The coding theory has been an important role in the constructing of secret sharing schemes. It is known that every lin...Secret sharing is an important topic in cryptography and has applications in information security. The coding theory has been an important role in the constructing of secret sharing schemes. It is known that every linear code can be used to construct secret sharing schemes. So, we use the parity-check matrix of a linear code to construct secret sharing schemes based on linear codes. We also describe some techniques to recover the secret and determine the access structure of the new scheme. In this paper, we use the Massey＇s secret sharing scheme.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 61072071)
文摘Quantum secret sharing（QSS） is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2k- 1, 1, k] quantum error-correcting code （QECC） to implement a quantum （k, 2k-1） threshold scheme. It also takes advantage of classical enhancement of the [2k-1, 1, k] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously. Because information is encoded into QECC, these schemes can prevent intercept-resend attacks and be implemented on some noisy channels.
文摘Linear dispersion codes (LDCs) were originally designed based on maximum likelihood detection. They do not have good performance when using ordered successive interference cancellation (OSIC) detection. In this paper,we propose a new improved linear dispersion codes transmission scheme to combat performance loss of original LDCs when using OSIC detection. We introduce an interleaver to each data substream transmitted over different antennas after LDCs encoder. Furthermore,a new computer search criterion for a linear transformation matrix is also proposed. New search criterion is to minimize the symbol error rate based on OSIC detection. Computer simulations show that the performance of proposed LDCs transmission scheme is better than the original LDCs.
基金supported by the National Natural Science Foundation of China(61171170) the Natural Science Foundation of Anhui Province(1408085QF115)
文摘This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block code share the propertyof linear correlation, the existing linear correlation-basedidentification method is invalid for this case. This drawback can becircumvented by introducing a novel multi-fractal spectrum-basedmethod. Simulation results show that the new method has highrobustness and under the same conditions of bit error, the lowerthe code rate, the higher the recognition rate. Thus, the methodhas significant potential for future application in engineering.
基金This work was supported in part by the National Science Foundation of China(No.61772539,6187212,61972405),STITSX(No.201705D131025),1331KITSX,and CiCi3D.
文摘Stereolithographic(STL)files have been extensively used in rapid prototyping industries as well as many other fields as watermarking algorithms to secure intellectual property and protect three-dimensional models from theft.However,to the best of our knowledge,few studies have looked at how watermarking can resist attacks that involve vertex-reordering.Here,we present a lossless and robust watermarking scheme for STL files to protect against vertexreordering attacks.Specifically,we designed a novel error-correcting code(ECC)that can correct the error of any one-bit in a bitstream by inserting several check digits.In addition,ECC is designed to make use of redundant information according to the characteristics of STL files,which introduces further robustness for defense against attacks.No modifications are made to the geometric information of the three-dimensional model,which respects the requirements of a highprecision model.The experimental results show that the proposed watermarking scheme can survive numerous kinds of attack,including rotation,scaling and translation(RST),facet reordering,and vertex-reordering attacks.
基金Supported by Research Funds of Hubei Province(D20144401,Q20174503)。
文摘In this paper,we first generalize the constant dimension and orbit codes over finite fields to the constant rank and orbit codes over finite chain rings.Then we provide a relationship between constant rank codes over finite chain rings and constant dimension codes over the residue fields.In particular,we prove that an orbit submodule code over a finite chain ring is a constant rank code.Finally,for special finite chain ring F_(q)+γF_(q),we define a Gray mapφfrom(F_(q)+γF_(q))^(n)to F^(2n)_(q),and by using cyclic codes over F_(q)+γF_(q),we obtain a method of constructing an optimum distance constant dimension code over F_(q).
基金supported by Natural Science Foundation of China (No.61271258)
文摘In this work, the homomorphism of the classic linear block code in linear network coding for the case of binary field and its extensions is studied. It is proved that the classic linear error-control block code is homomorphic network error-control code in network coding. That is, if the source packets at the source node for a linear network coding are precoded using a linear block code, then every packet flowing in the network regarding to the source satisfies the same constraints as the source. As a consequence, error detection and correction can be performed at every intermediate nodes of multicast flow, rather than only at the destination node in the conventional way, which can help to identify and correct errors timely at the error-corrupted link and save the cost of forwarding error-corrupted data to the destination node when the intermediate nodes are ignorant of the errors. In addition, three examples are demonstrated which show that homomorphic linear code can be combined with homomorphic signature, McEliece public-key cryptosystem and unequal error protection respectively and thus have a great potential of practical utility.
基金She was with the Department of Mathematics in Wuhan University while writting this paper.
文摘Abraham Lempel et al made a connection between linear codes and systems of bilinear forms over finite fields. In this correspondence, a new simple proof of a theorem in [1] is presented; in addition, the encoding process and the decoding procedure of RS codes are simplified via circulant matrices. Finally, the results show that the correspondence between bilinear forms and linear codes is not unique.
文摘Let F_qbe afinite field with q=pmelements,where pis an odd prime and mis apositive integer.Here,let D_0={(x_1,x_2)∈F_q^2\{(0,0)}:Tr(x_1^(pk1+1)+x_2^(pk2+1))=c},where c∈F_q,Tr is the trace function fromFF_qtoFpand m/(m,k_1)is odd,m/(m,k_2)is even.Define ap-ary linear code C_D =c(a_1,a_2):(a_1,a_2)∈F_q^2},where c(a_1,a_2)=(Tr(a_1x_1+a_2x_2))_((x1,x2)∈D).At most three-weight distributions of two classes of linear codes are settled.
文摘The optimal and suboptimal structured algorithms of linear block codes from the geometrical perspective are represented.The minimum distance and weight property lemmas and the theorem are proved for the generator matrix.Based upon the property of generator matrix,the structured algorithms of linear block codes are demonstrated.Since the complexity of optimal structured algorithm is very high,the binary linear block codes is searched by using the suboptimal structured algorithm.The comparison with Bose-Chaudhuri-Hocquenqhem（BCH） codes shows that the searched linear block codes are equivalent on minimum distance and can be designed for more block lengths.Because the linear block codes are used widely in communication systems and digital applications,the optimal and suboptimal structured algorithms must have great future being widely used in many applications and perspectives.
文摘The binary extended Golay code has a two-level structure, which can be used in the decoding of the code. However, such structure is not limited to the Golay code, in fact, several binary linear codes can be constructed by a projective method which is related to the structure. In this correspondence, the binary (4n,n + 2k, ≥min(8, n,2d)) linear codes are resulted from quaternary (n,k,d) linear block codes. Based on the structure, the efficient maximum likelihood decoding algorithms can be presented correspondingly for the derived codes.
文摘Firstly,the Fourier transforms in finite fields and the concept of linear complexityof sequences are described.Then several known lower bounds on the minimum distance of cycliccodes are outlined.Finally,the minimum distance of cyclic codes is analyzed via linear complexityof sequences,and new theorems about the lower bounds are obtained.
基金Sponsored by the "111" Project of China (B08038)Important National Science & Technology Specific Projects (2009ZX03003-003+2 种基金2009ZX03003-004) the NSFC-Guangdong (U0635003)Program for Changjiang Scholars and Innovative Research Team in University(IRT0852)
文摘A new architecture of space-time codes as a combination of orthogonal space-time block codes （OSTBC） and linear dispersion codes （LDC） is proposed in order to improve the bit error rate（BER） performance of OSTBC.The scheme proposed is named linear dispersion orthogonal space-time block codes （LDOSTBC）.In LDOSTBC scheme,firstly,the data is coded into LDC codewords.Then,the coded LDC substreams are coded into OSTBC codewords again.The decoding algorithm of LDOSTBC combines linear decoding of OSTBC and ML decoding or suboptimum detection algorithms of LDC.Compared with OSTBC scheme when the rate of LDC is MtR,the performance of LDOSTBC scheme can be improved without decreasing the data rate,where Mt is the number of transmit antennas and R is the spectral efficiency of the modulation constellation.If some rate penalty is allowed,when the rate of LDC is less than MtR the performance of LDOSTBC can be improved further.
基金Supported by the National Natural Science Foundation of China (11271237)
文摘In this paper, we propose a novel space efficient secret sharing scheme on the basis of minimal linear codes, which satisfies the definition of a computationally efficient secret sharing scheme. In the scheme, we partition the underlying minimal linear code into disjoint classes, establishing a one-to-one correspondence between the minimal authorized subsets of participants and the representative codewords of all different classes. Each participant, with only one short share transmitted through a public channel, can share a large secret. Therefore, the proposed scheme can distribute a large secret in practical applications such as secure information dispersal in sensor networks and secure multiparty computation.
基金Supported by Trans-century Training Program Foundation for the Talents by the State Education Commission
文摘This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theory and the modern cryptography.
基金Supported by the Scientific Research Foundation of Hubei Provincial Education Department of China(Q20174503)the National Science Foundation of Hubei Polytechnic University of China(12xjz14A and 17xjz03A)。
文摘In this paper,we first give the definition of the Euclidean sums of linear codes,and prove that the Euclidean sums of linear codes are Euclidean dual-containing.Then we construct two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of the Reed-Solomon codes,and two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of linear codes generated by Vandermonde matrices over finite fields.Moreover,these optimal asymmetric quantum errorcorrecting codes constructed in this paper are different from the ones in the literature.
基金Supported by the National Program on Basic Sciences(973 Program,G19990751Q2)
文摘m-weight,as a new generalization of classical Hamming weight,was discussedin this paper.A condition for the existence of linear codes of certain m-weights was given;theSingleton bound,Plotkin bound and Sphere Parking bound of Hamming weight were correspondinglygeneralized to the m-weight.
文摘Genetic algorithms offer very good performances for solving large optimization problems, especially in the domain of error-correcting codes. However, they have a major drawback related to the time complexity and memory occupation when running on a uniprocessor computer. This paper proposes a parallel decoder for linear block codes, using parallel genetic algorithms (PGA). The good performance and time complexity are confirmed by theoretical study and by simulations on BCH(63,30,14) codes over both AWGN and flat Rayleigh fading channels. The simulation results show that the coding gain between parallel and single genetic algorithm is about 0.7 dB at BER = 10﹣5 with only 4 processors.
文摘Deep holes are very important in the decoding of generalized RS codes, and deep holes of RS codes have been widely studied, but there are few works on constructing general linear codes based on deep holes. Therefore, we consider constructing binary linear codes by combining deep holes with binary BCH codes. In this article, we consider the 2-error-correcting binary primitive BCH codes and the extended codes to construct new binary linear codes by combining them with deep holes, respectively. Furthermore, three classes of binary linear codes are constructed, and then we determine the parameters and the weight distributions of these new binary linear codes.
文摘In this paper, error-correction coding (ECC) in Gray codes is considered and its performance in the protecting of spatial image watermarks against lossy data compression is demonstrated. For this purpose, the differences between bit patterns of two Gray codewords are analyzed in detail. On the basis of the properties, a method for encoding watermark bits in the Gray codewords that represent signal levels by a single-error-correcting (SEC) code is developed, which is referred to as the Gray-ECC method in this paper. The two codewords of the SEC code corresponding to respective watermark bits are determined so as to minimize the expected amount of distortion caused by the watermark embedding. The stochastic analyses show that an error-correcting capacity of the Gray-ECC method is superior to that of the ECC in natural binary codes for changes in signal codewords. Experiments of the Gray-ECC method were conducted on 8-bit monochrome images to evaluate both the features of watermarked images and the performance of robustness for image distortion resulting from the JPEG DCT-baseline coding scheme. The results demonstrate that, compared with a conventional averaging-based method, the Gray-ECC method yields watermarked images with less amount of signal distortion and also makes the watermark comparably robust for lossy data compression.
文摘Secret sharing is an important topic in cryptography and has applications in information security. The coding theory has been an important role in the constructing of secret sharing schemes. It is known that every linear code can be used to construct secret sharing schemes. So, we use the parity-check matrix of a linear code to construct secret sharing schemes based on linear codes. We also describe some techniques to recover the secret and determine the access structure of the new scheme. In this paper, we use the Massey＇s secret sharing scheme.
