• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Designs, Codes and Crytography >Quasi-abelian codes
【24h】

Quasi-abelian codes

机译：准阿贝尔密码

获取原文
获取原文并翻译 | 示例
       
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

We study H-quasi-abelian codes in F_q[G], where H ≤ G are abelian groups such that gcd(|H|, q)=1. Such codes are generalizations of quasi-cyclic codes and can be viewed as linear codes over the group ring F_q[H]. Using the Discrete Fourier Transform, F_q [H] can be decomposed as a direct product of finite fields. This decomposition leads us to a structural characterization of quasi-abelian codes and their duals. Necessary and sufficient conditions for such codes to be self-dual are given together with the enumeration based on q-cyclotomic classes of H. In particular, when H is an elementary p-group, we characterize the q-cyclotomic classes of H and give an explicit formula for the number of self-dual H-quasi abelian codes. Analogous to 1-generator quasi-cyclic codes, we investigate the structural characterization and enumeration of 1-generator quasi-abelian codes. We show that the class of binary self-dual (strictly) quasi-abelian codes is asymptotically good. Finally, we present four strictly quasi-abelian codes and ten codes obtained by puncturing and shortening of these codes, whose minimum distances are better than the lower bound in Grassl's online table.
机译：我们研究F_q [G]中的H-拟阿贝尔编码，其中H≤G是阿贝尔群，使得gcd（| H |，q）= 1。这样的代码是准循环代码的一般化，可以看作组环F_q [H]上的线性代码。使用离散傅立叶变换，可以将F_q [H]分解为有限域的直接积。这种分解导致我们对准阿贝尔编码及其对偶进行结构表征。给出此类代码为对偶的充要条件，并给出基于H的q-环原子类的枚举。特别是，当H是基本p-基团时，我们表征H的q-环原子类，并给出自对偶H拟阿贝尔代码数目的显式公式。类似于1-generator准循环码，我们研究1-generator准阿贝尔编码的结构特征和枚举。我们证明了二进制自对偶（严格）拟阿贝尔编码的类在渐近性上是好的。最后，我们给出了四个严格的准阿贝尔密码和十个通过打孔和缩短这些密码而得到的密码，它们的最小距离比格拉斯在线表的下限更好。

著录项

  • 来源
    《Designs, Codes and Crytography》 |2015年第3期|511-531|共21页
  • 作者

    Somphong Jitman; San Ling;

  • 作者单位

    Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom 73000, Thailand,Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Republic of Singapore;

    Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Republic of Singapore;

  • 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

    Quasi-abelian codes; Group algebras; Discrete Fourier transform; Self-dual codes; 1-Generator quasi-abelian codes;

    机译：准阿贝尔密码;群代数;离散傅立叶变换;自对码;1生成器准阿贝尔编码;

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号