A note on linear complementary pairs of group codes

被引：11

作者：

Borello, Martino ^{[1
]}

de la Cruz, Javier ^{[2
]}

Willems, Wolfgang ^{[2
,3
]}

机构：

[1] Univ Paris 08, Lab Geometrie Anal & Applicat, Univ Sorbonne Paris Nord, LAGA,CNRS,UMR 7539, F-93430 Villetaneuse, France

[2] Univ Norte, Barranquilla, Colombia

[3] Otto von Guericke Univ, Magdeburg, Germany

来源：

DISCRETE MATHEMATICS | 2020年 / 343卷 / 08期

关键词：

Group code; Linear complementary pair (LCP);

D O I：

10.1016/j.disc.2020.111905

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a short and elementary proof of the fact that for a linear complementary pair (C, D), where C and D are 2-sided ideals in a group algebra, D is uniquely determined by C and the dual code D-perpendicular to is permutation equivalent to C. This includes earlier results of Carlet (2018) and aineri (2018) on nD cyclic codes which have been proved by subtle and lengthy calculations in the space of polynomials. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：3

共 9 条

[1]

Bringer J, 2014, LECT NOTES COMPUT SC, V8501, P40, DOI 10.1007/978-3-662-43826-8_4

[2] On Linear Complementary Pairs of Codes [J].

Carlet, Claude ;

Guneri, Cem ;

Ozbudak, Ferruh ;

Ozkaya, Buket ;

Sole, Patrick .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2018, 64 (10) :6583-6589

[3] Complementary Dual Codes for Counter-Measures to Side-Channel Attacks [J].

Carlet, Claude ;

Guilley, Sylvain .

CODING THEORY AND APPLICATIONS, 4TH INTERNATIONAL CASTLE MEETING, 2015, 3 :97-105

[4] On group codes with complementary duals [J].

de la Cruz, Javier ;

Willems, Wolfgang .

DESIGNS CODES AND CRYPTOGRAPHY, 2018, 86 (09) :2065-2073

[5] On Linear Complementary Pair of nD Cyclic Codes [J].

Guneri, Cem ;

Ozkaya, Buket ;

Sayici, Selcen .

IEEE COMMUNICATIONS LETTERS, 2018, 22 (12) :2404-2406

[6] LINEAR CODES WITH COMPLEMENTARY DUALS [J].

MASSEY, JL .

DISCRETE MATHEMATICS, 1992, 106 :337-342

[7] ON A CONJECTURE OF P-LANDROCK [J].

OKUYAMA, T ;

TSUSHIMA, Y .

JOURNAL OF ALGEBRA, 1986, 104 (01) :203-208

[8] A note on self-dual group codes [J].

Willems, W .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2002, 48 (12) :3107-3109

[9]

Ngo XT, 2015, 2015 IEEE INTERNATIONAL SYMPOSIUM ON HARDWARE ORIENTED SECURITY AND TRUST (HOST), P82, DOI 10.1109/HST.2015.7140242

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