Optimal binary codes from trace codes over a non-chain ring

被引：27
|
作者：
Shi, Minjia [1 ,2 ,3 ]
Liu, Yan [3 ]
Sole, Patrick [4 ]
机构：
[1] Anhui Univ, Key Lab Intelligent Comp & Signal Proc, Minist Educ, 3 Feixi Rd, Hefei 230039, Anhui, Peoples R China
[2] Southeast Univ, Natl Mobile Commun Res Lab, Nanjing 210096, Jiangsu, Peoples R China
[3] Anhui Univ, Sch Math Sci, Hefei 230601, Peoples R China
[4] Univ Paris 08, CNRS LAGA, F-93526 St Denis, France
来源：
DISCRETE APPLIED MATHEMATICS | 2017年 / 219卷
关键词：
Two-weight codes; Griesmer bound; Trace codes; Secret sharing schemes;
D O I：
10.1016/j.dam.2016.09.050
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We construct an infinite family of two-Lee-weight codes over the ring F-2 + uF(2) + vF(2) uvF(2). These codes are defined as trace codes and have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using character sums. Then, taking Gray mapping, we obtain an infinite family of abelian binary two-weight codes which are shown to be optimal by application of the Griesmer bound. Moreover, an application to secret sharing schemes is given. (C) 2016 Elsevier B.V. All rights reserved.
引用
收藏
页码：176 / 181
页数：6
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