Cyclic codes form an important class of codes. They have very interesting algebraic structure. Furthermore, they are equivalent to many important codes, such as binary Hamming codes, Golay codes and BCH codes. Minimal...Cyclic codes form an important class of codes. They have very interesting algebraic structure. Furthermore, they are equivalent to many important codes, such as binary Hamming codes, Golay codes and BCH codes. Minimal codewords in linear codes are widely used in constructing decoding algorithms and studying linear secret sharing scheme. In this paper, we show that in the binary cyclic code all of the codewords are minimal, except 0 and 1. Then, we obtain a result about the number of minimal codewords in the binary cyclic codes.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
Secret sharing has been a subject of study for over 30 years. The coding theory has been an important role in the constructing of the secret sharing schemes. It is known that every linear code can be used to construct...Secret sharing has been a subject of study for over 30 years. The coding theory has been an important role in the constructing of the secret sharing schemes. It is known that every linear code can be used to construct the secret sharing schemes. Since the code of a symmetric （V, k, λ）-design is a linear code, this study is about the secret sharing schemes based on C of Fp-code C of asymmetric （v, k, λ）-design.展开更多
A （t, n）--secret sharing scheme is a method of distribution of information among n participants such that t 〉 1 can reconstruct the secret but （t - 1） cannot. We explore some （k, n）--secret sharing schemes base...A （t, n）--secret sharing scheme is a method of distribution of information among n participants such that t 〉 1 can reconstruct the secret but （t - 1） cannot. We explore some （k, n）--secret sharing schemes based on the finite fields.展开更多
In this paper, we show that if Wmax 〈 6 for the Hamming code Ham （r, 2）, then all of the nonzero codewords of Ham （r, 2） are minimal and if Wrnax 〈 8 for the extended Hamming code Hfim （r, 2）, then all of the ...In this paper, we show that if Wmax 〈 6 for the Hamming code Ham （r, 2）, then all of the nonzero codewords of Ham （r, 2） are minimal and if Wrnax 〈 8 for the extended Hamming code Hfim （r, 2）, then all of the nonzero codewords ofHfim （r, 2） are minimal, where Wmax is the maximum nonzero weight in Ham （r, 2） and Hfim （r, 2）.展开更多
文摘Cyclic codes form an important class of codes. They have very interesting algebraic structure. Furthermore, they are equivalent to many important codes, such as binary Hamming codes, Golay codes and BCH codes. Minimal codewords in linear codes are widely used in constructing decoding algorithms and studying linear secret sharing scheme. In this paper, we show that in the binary cyclic code all of the codewords are minimal, except 0 and 1. Then, we obtain a result about the number of minimal codewords in the binary cyclic codes.
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.
文摘Secret sharing has been a subject of study for over 30 years. The coding theory has been an important role in the constructing of the secret sharing schemes. It is known that every linear code can be used to construct the secret sharing schemes. Since the code of a symmetric （V, k, λ）-design is a linear code, this study is about the secret sharing schemes based on C of Fp-code C of asymmetric （v, k, λ）-design.
文摘A （t, n）--secret sharing scheme is a method of distribution of information among n participants such that t 〉 1 can reconstruct the secret but （t - 1） cannot. We explore some （k, n）--secret sharing schemes based on the finite fields.
文摘In this paper, we show that if Wmax 〈 6 for the Hamming code Ham （r, 2）, then all of the nonzero codewords of Ham （r, 2） are minimal and if Wrnax 〈 8 for the extended Hamming code Hfim （r, 2）, then all of the nonzero codewords ofHfim （r, 2） are minimal, where Wmax is the maximum nonzero weight in Ham （r, 2） and Hfim （r, 2）.
