SEVERAL NEW CLASSES OF OPTIMAL TERNARY CYCLIC CODES WITH MINIMUM DISTANCE FOUR

被引：0

作者：

Wang, Lisha ^{[1
]}

Li, Nian ^{[1
]}

Xu, Linjie ^{[2
]}

Hu, Zhao ^{[1
]}

Zeng, Xiangyong ^{[1
]}

Nie, Liujie ^{[1
]}

机构：

[1] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China

[2] Wuhan Maritime Commun Res Inst, Wuhan 430079, Peoples R China

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2022年 / 16卷 / 04期

关键词：

Cyclic code; linear code; optimal code; sphere packing bound;

D O I：

暂无

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Let C-(u,C-v) denote the ternary cyclic code with two zeros alpha(u) and alpha(v), where alpha is a generator of F*(3m) and 1 <= u, v <= 3(m) - 1. In this paper, we first present a necessary and sufficient condition such that C-(u,C-v) is optimal with parameters [3(m) - 1, 3(m) - 1 - 2m, 4]. Further, based on this condition, we obtain several new classes of optimal ternary cyclic codes C-(u,C-v) with parameters [3(m) - 1, 3(m) - 1 - 2m, 4]. We show that these codes are new compared with the known results.

引用

页码：1001 / 1010

页数：10

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