l-LIPs of codes over finite chain rings

被引：4

作者：

Liu, Xiusheng ^{[1
]}

Hu, Peng ^{[2
]}

机构：

[1] Hubei Normal Univ, Sch Sci & Technol, Coll Arts & Sci, Huangshi 435109, Hubei, Peoples R China

[2] Hubei Polytech Univ, Sch Math & Phys, Huangshi 435003, Hubei, Peoples R China

来源：

DISCRETE MATHEMATICS | 2022年 / 345卷 / 12期

关键词：

l-LIPs of codes; Chain rings; l-Cyclicintersection pair of codes; Rank of linear codes; PAIRS;

D O I：

10.1016/j.disc.2022.113087

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we first generalize the l-linear intersection pair (l-LIP) of codes over finite fields to the linear l-intersection pair of codes over finite chain rings. Then three criteria of l-linear intersection pair of codes over finite chain rings are obtained. By means of the generator set of cyclic codes, we obtain the generator set of the intersection of two cyclic codes which helps us to get a characterization of l-cyclic intersection pair of codes. As an application, l-cyclic intersection pair of codes over finite chain rings are used to construct new entanglement-assisted quantum error correcting codes. Finally, under suitable conditions, we also obtain a characterization for a l-cyclic intersection pair of codes over principal ideal rings Z(k).

引用

页数：12

共 27 条

[1] Entanglement required in achieving entanglement-assisted channel capacities [J].

Bowen, G .

PHYSICAL REVIEW A, 2002, 66 (05) :8

[2] Correcting quantum errors with entanglement [J].

Brun, Todd ;

Devetak, Igor ;

Hsieh, Min-Hsiu .

SCIENCE, 2006, 314 (5798) :436-439

[3]

Carlet Claude, 2018, Arithmetic of Finite Fields. 7th International Workshop, WAIFI 2018. Revised Selected Papers: Lecture Notes in Computer Science (LNCS 11321), P95, DOI 10.1007/978-3-030-05153-2_5

[4] 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

[5] 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

[6] COMPLEMENTARY DUAL CODES FOR COUNTER-MEASURES TO SIDE-CHANNEL ATTACKS [J].

Carlet, Claude ;

Guilley, Sylvain .

ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2016, 10 (01) :131-150

[7]

Dougherty S. T., 2011, MATH J OKAYAMA U, V53, P39

[8] Independence of vectors in codes over rings [J].

Dougherty, Steven T. ;

Liu, Hongwei .

DESIGNS CODES AND CRYPTOGRAPHY, 2009, 51 (01) :55-68

[9]

Fan JH, 2016, QUANTUM INF COMPUT, V16, P423

[10] Entanglement-assisted quantum low-density parity-check codes [J].

Fujiwara, Yuichiro ;

Clark, David ;

Vandendriessche, Peter ;

De Boeck, Maarten ;

Tonchev, Vladimir D. .

PHYSICAL REVIEW A, 2010, 82 (04)

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