收稿日期: 2018-12-04
网络出版日期: 2021-04-27
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
Received date: 2018-12-04
Online published: 2021-04-27
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
卢啸华, 王永超, 丁洋 . 达到Gilbert-Varshamov界的准扭码[J]. 上海大学学报(自然科学版), 2021 , 27(2) : 289 -297 . DOI: 10.12066/j.issn.1007-2861.2129
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.
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