OPTIMAL THREE-WEIGHT CUBIC CODES

被引：0

作者：

Shi, Minjia ^{[1
,2
]}

Zhu, Hongwei ^{[1
,2
]}

Sole, Patrick ^{[3
]}

机构：

[1] Anhui Univ, Key Lab Intelligent Comp & Signal Proc, Minist Educ, 3 Feixi Rd, Hefei 230039, Anhui, Peoples R China

[2] Anhui Univ, Sch Math Sci, Hefei, Anhui, Peoples R China

[3] Univ Paris 08, CNRS, LAGA, 2 Rue Liberte, F-93526 St Denis, France

来源：

APPLIED AND COMPUTATIONAL MATHEMATICS | 2018年 / 17卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Trace Codes; Three-Weight Codes; Griesmer Bound; Secret Sharing Schemes; CONSTACYCLIC CODES;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we construct an infinite family of three-weight binary codes from linear codes over the ring R = F-2 + vF(2) + v(2)F(2)where v(3) = 1. These codes are defined as trace codes. They have the algebraic structure of abelian codes. Their Lee weight distributions are computed by employing character sums. The three-weight binary linear codes which we construct are shown to be optimal when m is odd and m > 1. They are cubic, that is to say quasi-cyclic of co-index three. An application to secret sharing schemes is given.

引用

页码：175 / 184

页数：10

共 20 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] Cubic self-dual binary codes [J].

Bonnecaze, A ;

Bracco, AD ;

Dougherty, ST ;

Nochefranca, LR ;

Solé, P .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2003, 49 (09) :2253-2259

[4]

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

[5]

CALDERBANK AR, 1984, PHILIPS J RES, V39, P143

[6] THE GEOMETRY OF 2-WEIGHT CODES [J].

CALDERBANK, R ;

KANTOR, WM .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1986, 18 :97-122

[7]

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

[8]

Ding C., 2011, DISCRETE MATH, V313, P434

[9]

Ding CS, 2003, LECT NOTES COMPUT SC, V2731, P11

[10] A Class of Two-Weight and Three-Weight Codes and Their Applications in Secret Sharing [J].

Ding, Kelan ;

Ding, Cunsheng .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2015, 61 (11) :5835-5842

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