The codes of formal power series rings R_∞=F[[r]]={sum from i=0 to ∞(a_lr^l|a_l∈F)}and finite chain rings R_i={a_0+a_1r+…+a_(i-1)r^(i-1)|a_i∈F}have close relationship in lifts and projection.In this paper,we stud...The codes of formal power series rings R_∞=F[[r]]={sum from i=0 to ∞(a_lr^l|a_l∈F)}and finite chain rings R_i={a_0+a_1r+…+a_(i-1)r^(i-1)|a_i∈F}have close relationship in lifts and projection.In this paper,we study self-dual codes over R_∞by means of self-dual codes over Ri,and give some characterizations of self-dual codes over R_∞.展开更多
In this paper, we discuss a kind of Hermitian inner product - symplectic inner product, which is different from the original inner product - Euclidean inner product. According to the definition of symplectic inner pro...In this paper, we discuss a kind of Hermitian inner product - symplectic inner product, which is different from the original inner product - Euclidean inner product. According to the definition of symplectic inner product, the codes under the symplectic inner product have better properties than those under the general Hermitian inner product. Here we present the necessary and sufficient condition for judging whether a linear code C over Fp with a generator matrix in the standard form is a symplectic self-dual code. In addition, we give a method for constructing a new symplectic self-dual codes over Fp, which is simpler than others.展开更多
A definition of a self-dual code on graph and a procedure based on factor graphs to judge a self-dual code were presented. Three contributions of this paper were described as follows. To begin with, transform T_ R→L ...A definition of a self-dual code on graph and a procedure based on factor graphs to judge a self-dual code were presented. Three contributions of this paper were described as follows. To begin with, transform T_ R→L were defined, which was the basis of self-dual codes defined on graphs and played a key role in the paper. The second were that a self-dual code could be defined on factor graph, which was much different from conventional algebraic method. The third was that a factor graph approach to judge a self-dual code was illustrated, which took advantage of duality properties of factor graphs and our proposed transform T_ R→L to offer a convenient and geometrically intuitive process to judge a self-dual code.展开更多
In this paper, we give an explicit construction for self-dual codes over F_p+vF_p(v^2= v) and determine all the self-dual codes over F_p+ vF_p by using self-dual codes over finite field F_p, where p is a prime.
In this paper, we construct MDS Euclidean self-dual codes which are ex-tended cyclic duadic codes. And we obtain many new MDS Euclidean self-dual codes. We also construct MDS Hermitian self-dual codes from generalized...In this paper, we construct MDS Euclidean self-dual codes which are ex-tended cyclic duadic codes. And we obtain many new MDS Euclidean self-dual codes. We also construct MDS Hermitian self-dual codes from generalized Reed-Solomon codes and constacyclic codes.展开更多
We give the structures of a cyclic code over ringR = F2 ＋ uF2 ＋ u^2F2 = {0, 1,u, u^2,v, v^2,uv, v^3},where u^3 = 0, of odd length and its dual code. For the cyclic code, necessary and sufficient conditions for the e...We give the structures of a cyclic code over ringR = F2 ＋ uF2 ＋ u^2F2 = {0, 1,u, u^2,v, v^2,uv, v^3},where u^3 = 0, of odd length and its dual code. For the cyclic code, necessary and sufficient conditions for the existence of self-dual code are provided.展开更多
In this paper, we study self-dual permutation codes over formal power series rings and finite principal ideal rings. We first give some results on the torsion codes associated with the linear codes over formal power s...In this paper, we study self-dual permutation codes over formal power series rings and finite principal ideal rings. We first give some results on the torsion codes associated with the linear codes over formal power series rings. These results allow for obtaining some conditions for non-existence of self-dual permutation codes over formal power series rings. Finally, we describe self-dual permutation codes over finite principal ideal rings by examining permutation codes over their component chain rings.展开更多
Permutation codes over finite chain rings are introduced; by using the character of the finite chain rings and the knowledge of representation of group, some conditions for existence or non-existence of self-dual perm...Permutation codes over finite chain rings are introduced; by using the character of the finite chain rings and the knowledge of representation of group, some conditions for existence or non-existence of self-dual permutation codes over finite chain rings are obtained. Specially, when the group is a direct product of a 2-group and a T-group, and the group action is transitive, the sufficient and necessary condition of the existence of permutation codes is given.展开更多
Let F_q be a finite field with q = p^m, where p is an odd prime. In this paper, we study the repeated-root self-dual negacyclic codes over Fq. The enumeration of such codes is investigated. We obtain all the self-dual...Let F_q be a finite field with q = p^m, where p is an odd prime. In this paper, we study the repeated-root self-dual negacyclic codes over Fq. The enumeration of such codes is investigated. We obtain all the self-dual negacyclic codes of length 2~ap^r over F_q, a ≥ 1.The construction of self-dual negacyclic codes of length 2~abp^r over F_q is also provided, where gcd（2, b） = gcd（b, p） = 1 and a ≥ 1.展开更多
In the article“Deep Learning-Enhanced Brain Tumor Prediction via Entropy-Coded BPSO in CIELAB Color Space”by Mudassir Khalil,Muhammad Imran Sharif,Ahmed Naeem,Muhammad Umar Chaudhry,Hafiz Tayyab Rauf,Adham E.Ragab C...In the article“Deep Learning-Enhanced Brain Tumor Prediction via Entropy-Coded BPSO in CIELAB Color Space”by Mudassir Khalil,Muhammad Imran Sharif,Ahmed Naeem,Muhammad Umar Chaudhry,Hafiz Tayyab Rauf,Adham E.Ragab Computers,Materials&Continua,2023,Vol.77,No.2,pp.2031–2047.DOI:10.32604/cmc.2023.043687,URL:https://www.techscience.com/cmc/v77n2/54831,there was an error regarding the affiliation for the author Hafiz Tayyab Rauf.Instead of“Centre for Smart Systems,AI and Cybersecurity,Staffordshire University,Stoke-on-Trent,ST42DE,UK”,the affiliation should be“Independent Researcher,Bradford,BD80HS,UK”.展开更多
A two-stage algorithm based on deep learning for the detection and recognition of can bottom spray codes and numbers is proposed to address the problems of small character areas and fast production line speeds in can ...A two-stage algorithm based on deep learning for the detection and recognition of can bottom spray codes and numbers is proposed to address the problems of small character areas and fast production line speeds in can bottom spray code number recognition.In the coding number detection stage,Differentiable Binarization Network is used as the backbone network,combined with the Attention and Dilation Convolutions Path Aggregation Network feature fusion structure to enhance the model detection effect.In terms of text recognition,using the Scene Visual Text Recognition coding number recognition network for end-to-end training can alleviate the problem of coding recognition errors caused by image color distortion due to variations in lighting and background noise.In addition,model pruning and quantization are used to reduce the number ofmodel parameters to meet deployment requirements in resource-constrained environments.A comparative experiment was conducted using the dataset of tank bottom spray code numbers collected on-site,and a transfer experiment was conducted using the dataset of packaging box production date.The experimental results show that the algorithm proposed in this study can effectively locate the coding of cans at different positions on the roller conveyor,and can accurately identify the coding numbers at high production line speeds.The Hmean value of the coding number detection is 97.32%,and the accuracy of the coding number recognition is 98.21%.This verifies that the algorithm proposed in this paper has high accuracy in coding number detection and recognition.展开更多
The care of a patient involved in major trauma with exsanguinating haemorrhage is time-critical to achieve definitive haemorrhage control,and it requires coordinated multidisciplinary care.During initial resuscitation...The care of a patient involved in major trauma with exsanguinating haemorrhage is time-critical to achieve definitive haemorrhage control,and it requires coordinated multidisciplinary care.During initial resuscitation of a patient in the emergency department(ED),Code Crimson activation facilitates rapid decisionmaking by multi-disciplinary specialists for definitive haemorrhage control in operating theatre(OT)and/or interventional radiology(IR)suite.Once this decision has been made,there may still be various factors that lead to delay in transporting the patient from ED to OT/IR.Red Blanket protocol identifies and addresses these factors and processes which cause delay,and aims to facilitate rapid and safe transport of the haemodynamically unstable patient from ED to OT,while minimizing delay in resuscitation during the transfer.The two processes,Code Crimson and Red Blanket,complement each other.It would be ideal to merge the two processes into a single protocol rather than having two separate workflows.Introducing these quality improvement strategies and coor-dinated processes within the trauma framework of the hospitals/healthcare systems will help in further improving the multi-disciplinary care for the complex trauma patients requiring rapid and definitive haemorrhage control.展开更多
Fraction repetition(FR)codes are integral in distributed storage systems(DSS)with exact repair-by-transfer,while pliable fraction repetition codes are vital for DSSs in which both the per-node storage and repetition d...Fraction repetition(FR)codes are integral in distributed storage systems(DSS)with exact repair-by-transfer,while pliable fraction repetition codes are vital for DSSs in which both the per-node storage and repetition degree can easily be adjusted simultaneously.This paper introduces a new type of pliable FR codes,called absolute balanced pliable FR(ABPFR)codes,in which the access balancing in DSS is considered.Additionally,the equivalence between pliable FR codes and resolvable transversal packings in combinatorial design theory is presented.Then constructions of pliable FR codes and ABPFR codes based on resolvable transversal packings are presented.展开更多
Multilevel coding(MLC)is a commonly used polar coded modulation scheme,but challenging to implement in engineering due to its high complexity and long decoding delay for high-order modulations.To address these limitat...Multilevel coding(MLC)is a commonly used polar coded modulation scheme,but challenging to implement in engineering due to its high complexity and long decoding delay for high-order modulations.To address these limitations,a novel two-level serially concatenated MLC scheme,in which the bitlevels with similar reliability are bundled and transmitted together,is proposed.The proposed scheme hierarchically protects the two bit-level sets:the bitlevel sets at the higher level are sufficiently reliable and do not require excessive resources for protection,whereas only the bit-level sets at the lower level are encoded by polar codes.The proposed scheme has the advantages of low power consumption,low delay and high reliability.Moreover,an optimized constellation signal labeling rule that can enhance the performance is proposed.Finally,the superiority of the proposed scheme is validated through the theoretical analysis and simulation results.Compared with the bit interleaving coding modulation(BICM)scheme,under 256-quadrature amplitude modulation(QAM),the proposed scheme attains a performance gain of 1.0 dB while reducing the decoding complexity by 54.55%.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
Neuroscience (also known as neurobiology) is a science that studies the structure, function, development, pharmacology and pathology of the nervous system. In recent years, C. Cotardo has introduced coding theory into...Neuroscience (also known as neurobiology) is a science that studies the structure, function, development, pharmacology and pathology of the nervous system. In recent years, C. Cotardo has introduced coding theory into neuroscience, proposing the concept of combinatorial neural codes. And it was further studied in depth using algebraic methods by C. Curto. In this paper, we construct a class of combinatorial neural codes with special properties based on classical combinatorial structures such as orthogonal Latin rectangle, disjoint Steiner systems, groupable designs and transversal designs. These neural codes have significant weight distribution properties and large minimum distances, and are thus valuable for potential applications in information representation and neuroscience. This study provides new ideas for the construction method and property analysis of combinatorial neural codes, and enriches the study of algebraic coding theory.展开更多
基金Foundation item： Supported by the Scientific Research Foundation of Hubei Provincial Education Depart- ment（B2013069） Supported by the National Science Foundation of Hubei Polytechnic University（12xjzl4A, 11yjz37B）
文摘The codes of formal power series rings R_∞=F[[r]]={sum from i=0 to ∞(a_lr^l|a_l∈F)}and finite chain rings R_i={a_0+a_1r+…+a_(i-1)r^(i-1)|a_i∈F}have close relationship in lifts and projection.In this paper,we study self-dual codes over R_∞by means of self-dual codes over Ri,and give some characterizations of self-dual codes over R_∞.
文摘In this paper, we discuss a kind of Hermitian inner product - symplectic inner product, which is different from the original inner product - Euclidean inner product. According to the definition of symplectic inner product, the codes under the symplectic inner product have better properties than those under the general Hermitian inner product. Here we present the necessary and sufficient condition for judging whether a linear code C over Fp with a generator matrix in the standard form is a symplectic self-dual code. In addition, we give a method for constructing a new symplectic self-dual codes over Fp, which is simpler than others.
基金The National Natural Science Foundation of China (No60472018)
文摘A definition of a self-dual code on graph and a procedure based on factor graphs to judge a self-dual code were presented. Three contributions of this paper were described as follows. To begin with, transform T_ R→L were defined, which was the basis of self-dual codes defined on graphs and played a key role in the paper. The second were that a self-dual code could be defined on factor graph, which was much different from conventional algebraic method. The third was that a factor graph approach to judge a self-dual code was illustrated, which took advantage of duality properties of factor graphs and our proposed transform T_ R→L to offer a convenient and geometrically intuitive process to judge a self-dual code.
基金supported in part by the National Science Foundation of China under Grant 11571005in part by the Key Research Project of Higher Education of the Education Department of Henan Province under Grant 19A120010
文摘In this paper, we give an explicit construction for self-dual codes over F_p+vF_p(v^2= v) and determine all the self-dual codes over F_p+ vF_p by using self-dual codes over finite field F_p, where p is a prime.
文摘In this paper, we construct MDS Euclidean self-dual codes which are ex-tended cyclic duadic codes. And we obtain many new MDS Euclidean self-dual codes. We also construct MDS Hermitian self-dual codes from generalized Reed-Solomon codes and constacyclic codes.
文摘We give the structures of a cyclic code over ringR = F2 ＋ uF2 ＋ u^2F2 = {0, 1,u, u^2,v, v^2,uv, v^3},where u^3 = 0, of odd length and its dual code. For the cyclic code, necessary and sufficient conditions for the existence of self-dual code are provided.
文摘In this paper, we study self-dual permutation codes over formal power series rings and finite principal ideal rings. We first give some results on the torsion codes associated with the linear codes over formal power series rings. These results allow for obtaining some conditions for non-existence of self-dual permutation codes over formal power series rings. Finally, we describe self-dual permutation codes over finite principal ideal rings by examining permutation codes over their component chain rings.
基金Supported by the National Natural Science Foundation of China (60373087, 60473023, 90104005, 60673071)
文摘Permutation codes over finite chain rings are introduced; by using the character of the finite chain rings and the knowledge of representation of group, some conditions for existence or non-existence of self-dual permutation codes over finite chain rings are obtained. Specially, when the group is a direct product of a 2-group and a T-group, and the group action is transitive, the sufficient and necessary condition of the existence of permutation codes is given.
基金Supported by Reward Fund for Outstanding Young and Middle-Aged Scientists of Shandong Province(Grant No.BS2011DX011)Qingdao Postdoctoral Fund(Grant No.861605040007)
文摘Let F_q be a finite field with q = p^m, where p is an odd prime. In this paper, we study the repeated-root self-dual negacyclic codes over Fq. The enumeration of such codes is investigated. We obtain all the self-dual negacyclic codes of length 2~ap^r over F_q, a ≥ 1.The construction of self-dual negacyclic codes of length 2~abp^r over F_q is also provided, where gcd（2, b） = gcd（b, p） = 1 and a ≥ 1.
文摘In the article“Deep Learning-Enhanced Brain Tumor Prediction via Entropy-Coded BPSO in CIELAB Color Space”by Mudassir Khalil,Muhammad Imran Sharif,Ahmed Naeem,Muhammad Umar Chaudhry,Hafiz Tayyab Rauf,Adham E.Ragab Computers,Materials&Continua,2023,Vol.77,No.2,pp.2031–2047.DOI:10.32604/cmc.2023.043687,URL:https://www.techscience.com/cmc/v77n2/54831,there was an error regarding the affiliation for the author Hafiz Tayyab Rauf.Instead of“Centre for Smart Systems,AI and Cybersecurity,Staffordshire University,Stoke-on-Trent,ST42DE,UK”,the affiliation should be“Independent Researcher,Bradford,BD80HS,UK”.
文摘A two-stage algorithm based on deep learning for the detection and recognition of can bottom spray codes and numbers is proposed to address the problems of small character areas and fast production line speeds in can bottom spray code number recognition.In the coding number detection stage,Differentiable Binarization Network is used as the backbone network,combined with the Attention and Dilation Convolutions Path Aggregation Network feature fusion structure to enhance the model detection effect.In terms of text recognition,using the Scene Visual Text Recognition coding number recognition network for end-to-end training can alleviate the problem of coding recognition errors caused by image color distortion due to variations in lighting and background noise.In addition,model pruning and quantization are used to reduce the number ofmodel parameters to meet deployment requirements in resource-constrained environments.A comparative experiment was conducted using the dataset of tank bottom spray code numbers collected on-site,and a transfer experiment was conducted using the dataset of packaging box production date.The experimental results show that the algorithm proposed in this study can effectively locate the coding of cans at different positions on the roller conveyor,and can accurately identify the coding numbers at high production line speeds.The Hmean value of the coding number detection is 97.32%,and the accuracy of the coding number recognition is 98.21%.This verifies that the algorithm proposed in this paper has high accuracy in coding number detection and recognition.
文摘The care of a patient involved in major trauma with exsanguinating haemorrhage is time-critical to achieve definitive haemorrhage control,and it requires coordinated multidisciplinary care.During initial resuscitation of a patient in the emergency department(ED),Code Crimson activation facilitates rapid decisionmaking by multi-disciplinary specialists for definitive haemorrhage control in operating theatre(OT)and/or interventional radiology(IR)suite.Once this decision has been made,there may still be various factors that lead to delay in transporting the patient from ED to OT/IR.Red Blanket protocol identifies and addresses these factors and processes which cause delay,and aims to facilitate rapid and safe transport of the haemodynamically unstable patient from ED to OT,while minimizing delay in resuscitation during the transfer.The two processes,Code Crimson and Red Blanket,complement each other.It would be ideal to merge the two processes into a single protocol rather than having two separate workflows.Introducing these quality improvement strategies and coor-dinated processes within the trauma framework of the hospitals/healthcare systems will help in further improving the multi-disciplinary care for the complex trauma patients requiring rapid and definitive haemorrhage control.
基金Supported in part by the National Key R&D Program of China(No.2020YFA0712300)NSFC(No.61872353)。
文摘Fraction repetition(FR)codes are integral in distributed storage systems(DSS)with exact repair-by-transfer,while pliable fraction repetition codes are vital for DSSs in which both the per-node storage and repetition degree can easily be adjusted simultaneously.This paper introduces a new type of pliable FR codes,called absolute balanced pliable FR(ABPFR)codes,in which the access balancing in DSS is considered.Additionally,the equivalence between pliable FR codes and resolvable transversal packings in combinatorial design theory is presented.Then constructions of pliable FR codes and ABPFR codes based on resolvable transversal packings are presented.
基金supported by the External Cooperation Program of Science and Technology of Fujian Province,China(2024I0016)the Fundamental Research Funds for the Central Universities(ZQN-1005).
文摘Multilevel coding(MLC)is a commonly used polar coded modulation scheme,but challenging to implement in engineering due to its high complexity and long decoding delay for high-order modulations.To address these limitations,a novel two-level serially concatenated MLC scheme,in which the bitlevels with similar reliability are bundled and transmitted together,is proposed.The proposed scheme hierarchically protects the two bit-level sets:the bitlevel sets at the higher level are sufficiently reliable and do not require excessive resources for protection,whereas only the bit-level sets at the lower level are encoded by polar codes.The proposed scheme has the advantages of low power consumption,low delay and high reliability.Moreover,an optimized constellation signal labeling rule that can enhance the performance is proposed.Finally,the superiority of the proposed scheme is validated through the theoretical analysis and simulation results.Compared with the bit interleaving coding modulation(BICM)scheme,under 256-quadrature amplitude modulation(QAM),the proposed scheme attains a performance gain of 1.0 dB while reducing the decoding complexity by 54.55%.
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).
文摘Neuroscience (also known as neurobiology) is a science that studies the structure, function, development, pharmacology and pathology of the nervous system. In recent years, C. Cotardo has introduced coding theory into neuroscience, proposing the concept of combinatorial neural codes. And it was further studied in depth using algebraic methods by C. Curto. In this paper, we construct a class of combinatorial neural codes with special properties based on classical combinatorial structures such as orthogonal Latin rectangle, disjoint Steiner systems, groupable designs and transversal designs. These neural codes have significant weight distribution properties and large minimum distances, and are thus valuable for potential applications in information representation and neuroscience. This study provides new ideas for the construction method and property analysis of combinatorial neural codes, and enriches the study of algebraic coding theory.
