Journal of Shanghai University(Natural Science Edition) ›› 2021, Vol. 27 ›› Issue (2): 289-297.doi: 10.12066/j.issn.1007-2861.2129

• Research Articles • Previous Articles     Next Articles

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

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

CLC Number: