HIGHER WEIGHTS AND NEAR-MDR CODES OVER CHAIN RINGS

Liu Zihui; Liao Dajian

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HIGHER WEIGHTS AND NEAR-MDR CODES OVER CHAIN RINGS

机译：较高的重量和近MDR代码在链环上

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摘要

The matrix description of a near-MDR code is given, and some judging criterions are presented for near-MDR codes. We also give the weight distribution of a near-MDR code and the applications of a near-MDR code to secret sharing schemes. Furthermore, we will introduce the chain condition for free codes over finite chain rings, and then present a formula for computing higher weights of tensor product of free codes satisfying the chain condition. We will also find a chain for any near-MDR code, and thus show that any near-MDR code satisfies the chain condition.

机译：给出了近MDR码的矩阵描述，并且介绍了一些判断标准用于近MDR码。我们还提供了近MDR代码的重量分布以及近MDR代码的应用到秘密共享方案。此外，我们将引入有限链环上的免费代码的链条条件，然后提出一种用于计算满足链条条件的自由码的张量产物的更高权重的公式。我们还将找到任何近MDR代码的链条，从而显示任何近MDR代码满足链条状况。

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来源
《Advances in mathematics of communications》 |2018年第4期|共12页
作者
Liu Zihui; Liao Dajian;
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作者单位

Beijing Inst Technol Dept Math Beijing Key Lab MCAACI Beijing Peoples R China;

Huaihai Inst Technol Coll Sci Lianyungang 222005 Peoples R China;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
near-MDR code; secret sharing scheme; chain condition; tensor product; Generalized Hamming weight;

机译：近MDR码;秘密共享方案;链条状况;张量产品;广义汉明重;

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专利

1. HIGHER WEIGHTS AND NEAR-MDR CODES OVER CHAIN RINGS [J] . Liu Zihui, Liao Dajian Advances in mathematics of communications . 2018,第4期

机译：较高的重量和近MDR代码在链环上
2. MacWilliams identity for linear codes over finite chain rings with respect to homogeneous weight [J] . Mina Moeini, Rashid Rezaei, Karim Samei Bulletin of the Korean Mathematical Society . 2021,第5期

机译：用于线性码的MacWilliams标识，相对于均匀重量的有限链环
3. One-homogeneous weight codes over finite chain rings [J] . Mustafa Sari, Irfan Siap, Vedat Siap Bulletin of the Korean Mathematical Society . 2015,第6期

机译：有限链环上的一维权重代码
4. On Generalized Hamming Weights for Codes over Finite Chain Rings [C] . Hiroshi Horimoto, Keisuke Shiromoto Applied Algebra, Algebraic Algorithms and Error-Correcting Codes . 2001

机译：有限链环上代码的广义汉明权重
5. On p-adic estimates of weights in Abelian codes over Galois rings [D] . Katz, Daniel J. 2005

机译：关于Galois环上Abelian编码中权重的p-adic估计
6. Type II Myosin Heavy Chain Encoded by the myo2 Gene Composes the Contractile Ring during Cytokinesis in Schizosaccharomyces pombe [O] . Chikako Kitayama, Asako Sugimoto, Masayuki Yamamoto 1997

机译：myo2基因编码的II型肌球蛋白重链在粟酒裂殖酵母的胞质分裂过程中组成收缩环。
7. Higher weights and near-MDR codes over chain rings [O] . Zihui Liu, Dajian Liao 2018

机译：较高的重量和近mdr码覆盖环环
8. The weight hierarchies and chain condition of a class of codes from varieties over finite fields [R] . Wu, Xinen, Feng, Gui-Liang, Rao, T. R. N. 1996

机译：有限域上变种的一类代码的权重等级和链条件

HIGHER WEIGHTS AND NEAR-MDR CODES OVER CHAIN RINGS

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