Optimal Two-Weight Codes From Trace Codes Over F2 + uF2

被引：58

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, Hefei 230039, 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：

IEEE COMMUNICATIONS LETTERS | 2016年 / 20卷 / 12期

关键词：

Two-weight codes; codes over rings; Griesmer bound; secret sharing schemes;

D O I：

10.1109/LCOMM.2016.2614934

中图分类号：

TN [电子技术、通信技术];

学科分类号：

0809 ;

摘要：

We construct an infinite family of two-Lee-weight codes over the ring F-2 + uF(2). These codes are defined as trace codes. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using character sums. By Gray mapping, we obtain an infinite family of abelian binary two-weight codes. They are shown to be optimal by application of the Griesmer bound. An application to secret sharing schemes is given.

引用

页码：2346 / 2349

页数：4

共 16 条

[1]

[Anonymous], 1978, The Theory of Error-Correcting Codes

[2] Minimal vectors in linear codes [J].

Ashikhmin, A ;

Barg, A .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1998, 44 (05) :2010-2017

[3] Cyclic codes and self-dual codes over F2+uF2 [J].

Bonnecaze, A ;

Udaya, P .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1999, 45 (04) :1250-1255

[4] The Magma algebra system .1. The user language [J].

Bosma, W ;

Cannon, J ;

Playoust, C .

JOURNAL OF SYMBOLIC COMPUTATION, 1997, 24 (3-4) :235-265

[5]

Brouwer AE, 2012, UNIVERSITEXT, P1, DOI 10.1007/978-1-4614-1939-6

[6] Ring geometries, two-weight codes, and strongly regular graphs [J].

Byrne, Eimear ;

Greferath, Marcus ;

Honold, Thomas .

DESIGNS CODES AND CRYPTOGRAPHY, 2008, 48 (01) :1-16

[7] Properties of codes with two homogeneous weights [J].

Byrne, Eimear ;

Kiermaier, Michael ;

Sneyd, Alison .

FINITE FIELDS AND THEIR APPLICATIONS, 2012, 18 (04) :711-727

[8]

Delsarte Ph., 1972, Discrete Mathematics, V3, P47, DOI 10.1016/0012-365X(72)90024-6

[9]

Ding C., 2003, LECT NOTES COMPUTER, P1

[10] A BOUND FOR ERROR-CORRECTING CODES [J].

GRIESMER, JH .

IBM JOURNAL OF RESEARCH AND DEVELOPMENT, 1960, 4 (05) :532-542

← 1 2 →