上海大学学报(自然科学版) ›› 2021, Vol. 27 ›› Issue (2): 289-297.doi: 10.12066/j.issn.1007-2861.2129

• 研究论文 • 上一篇    下一篇

达到Gilbert-Varshamov界的准扭码

卢啸华, 王永超, 丁洋()   

  1. 上海大学 理学院, 上海 200444
  • 收稿日期:2018-12-04 出版日期:2021-04-30 发布日期:2021-04-27
  • 通讯作者: 丁洋 E-mail:dingyang@t.shu.edu.cn
  • 作者简介:丁 洋(1985—), 女, 副教授, 研究方向为编码密码学. E-mail:dingyang@t.shu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11671248)

Quasi-twisted codes achieving the Gilbert-Varshamov bound

LU Xiaohua, WANG Yongchao, DING Yang()   

  1. College of Sciences, Shanghai University, Shanghai 200444, China
  • Received:2018-12-04 Online:2021-04-30 Published:2021-04-27
  • Contact: DING Yang E-mail:dingyang@t.shu.edu.cn

摘要:

准扭码是循环码的一种推广, 1-生成准扭码同构于多项式剩余类环的1-生成子模. Gilbert-Varshamov界是衡量准扭码好坏的一个重要标准. 利用不可约多项式的性质得到任意的一个1-生成准扭码, 有很大概率渐进达到Gilbert-Varshamov界.

关键词: 循环码, Gilbert-Varshamov界, 不可约多项式, 准扭码

Abstract:

Quasi-twisted codes are regarded as a generalisation of cyclic codes. The Gilbert-Varshamov bound is an important criterion for measuring the quality of quasi-twisted codes. A class of randomized one-generator quasi-twisted codes was presented. Furthermore, it was proved that, using the properties of irreducible polynomials, random one-generator quasi-twisted codes asymptotically achieved the Gilbert-Varshamov bound with high probability and identified a one-generator module of a polynomial quotient ring.

Key words: cyclic codes, Gilbert-Varshamov bound, irreducible polynomials, quasi-twisted codes

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