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pro vyhledávání: '"Sun, Zhonghua"'
Recently, binary cyclic codes with parameters $[n,(n\pm1)/2,\geq \sqrt{n}]$ have been a hot topic since their minimum distances have a square-root bound. In this paper, we construct four classes of binary cyclic codes $\mathcal{C}_{\mathcal{S},0}$, $
Externí odkaz:
http://arxiv.org/abs/2408.01906
A generator matrix of a linear code $\C$ over $\gf(q)$ is also a matrix of the same rank $k$ over any extension field $\gf(q^\ell)$ and generates a linear code of the same length, same dimension and same minimum distance over $\gf(q^\ell)$, denoted b
Externí odkaz:
http://arxiv.org/abs/2407.15104
Constacyclic codes over finite fields are an important class of linear codes as they contain distance-optimal codes and linear codes with best known parameters. They are interesting in theory and practice, as they have the constacyclic structure. In
Externí odkaz:
http://arxiv.org/abs/2404.18438
Cyclic codes are an interesting family of linear codes since they have efficient decoding algorithms and contain optimal codes as subfamilies. Constructing infinite families of cyclic codes with good parameters is important in both theory and practic
Externí odkaz:
http://arxiv.org/abs/2310.20179
The classical way of extending an $[n, k, d]$ linear code $\C$ is to add an overall parity-check coordinate to each codeword of the linear code $\C$. This extended code, denoted by $\overline{\C}(-\bone)$ and called the standardly extended code of $\
Externí odkaz:
http://arxiv.org/abs/2307.08053
Autor:
Sun, Zhonghua, Ding, Cunsheng
A linear code with parameters $[n, k, n-k+1]$ is called a maximum distance separable (MDS for short) code. A linear code with parameters $[n, k, n-k]$ is said to be almost maximum distance separable (AMDS for short). A linear code is said to be near
Externí odkaz:
http://arxiv.org/abs/2307.04076
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in IEEE Trans.
Externí odkaz:
http://arxiv.org/abs/2303.06849
Autor:
Sun, Zhonghua, Ding, Cunsheng
Constacyclic codes contain cyclic codes as a subclass and have nice algebraic structures. Constacyclic codes have theoretical importance, as they are connected to a number of areas of mathematics and outperform cyclic codes in several aspects. Negacy
Externí odkaz:
http://arxiv.org/abs/2301.09783