Skew quasi-cyclic codes over Galois rings

Maheshanand Bhaintwal

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Skew quasi-cyclic codes over Galois rings

机译：Galois环上的偏准循环码

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Recently there has been a lot of interest on algebraic codes in the setting of skew polynomial rings. In this paper we have studied skew quasi-cyclic (QC) codes over Galois rings. We have given a necessary and sufficient condition for skew cyclic codes over Galois rings to be free, and determined a distance bound for free skew cyclic codes. A sufficient condition for 1-generator skew QC codes to be free is determined. Some distance bounds for free 1-generator skew QC codes are discussed. A canonical decomposition of skew QC codes is presented.

机译：最近，在倾斜多项式环的设置中，代数代码引起了很多兴趣。在本文中，我们研究了Galois环上的偏准循环（QC）码。我们给出了Galois环上的偏斜循环码是自由的充要条件，并确定了自由偏斜循环码的距离。确定使1-发电机偏斜QC代码自由的充分条件。讨论了自由1发生器偏斜QC码的一些距离范围。提出了偏斜QC码的规范分解。

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来源
《Designs, Codes and Crytography》 |2012年第1期|p.85-101|共17页
作者
Maheshanand Bhaintwal;
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作者单位

Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
skew polynomial rings; quasi-cyclic codes; galois rings;

机译：偏多项式环准循环码;伽罗瓦环;

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1. Skew cyclic and quasi-cyclic codes of arbitrary length over Galois rings [J] . Mingzhong Wu International journal of algebra . 2013,第17期

机译：Galois环上任意长度的偏周期和准周期码
2. Skew quasi-cyclic codes over Galois rings [J] . Maheshanand Bhaintwal Designs, Codes and Cryptography . 2012,第1期

机译：Galois环上的偏准循环码
3. Generalized quasi-cyclic codes over Galois rings: structural properties and enumeration [J] . Cao Yonglin Applicable algebra in engineering, communication and computing . 2011,第3期

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4. Construction of quasi-cyclic LDPC cycle codes over Galois Field GF(q) based on cycle entropy and application on patterned media storage [C] . Liu X., Xiong F., Yin Y. 2015 IEEE Magnetics Conference . 2015

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5. On p-adic estimates of weights in Abelian codes over Galois rings [D] . Katz, Daniel J. 2005

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6. A novel skew analysis reveals substitution asymmetries linked to genetic code GC-biases and PolIII a-subunit isoforms [O] . Konstantinos Apostolou-Karampelis, Christoforos Nikolaou, Yannis Almirantis 2016

机译：新颖的偏斜分析揭示了与遗传密码GC偏爱和PolIIIα亚基亚型相关的取代不对称性
7. Binary quasi-cyclic codes of index 2 and skew polynomial rings [O] . Solé Patrick, Yemen Olfa 2012

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8. Generalized hamming weighs for Galois ring linear codes [R] . Ashikhmin, A. 1997

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Skew quasi-cyclic codes over Galois rings

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