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Journal of Shanghai University >

2021 , Vol. 27 >Issue 2: 289 - 297

DOI: https://doi.org/10.12066/j.issn.1007-2861.2129

Research Articles

Quasi-twisted codes achieving the Gilbert-Varshamov bound

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  • College of Sciences, Shanghai University, Shanghai 200444, China

Received date: 2018-12-04

  Online published: 2021-04-27

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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

Cite this article

LU Xiaohua, WANG Yongchao, DING Yang . Quasi-twisted codes achieving the Gilbert-Varshamov bound[J]. Journal of Shanghai University, 2021 , 27(2) : 289 -297 . DOI: 10.12066/j.issn.1007-2861.2129

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