SOME RESULTS ON ZpZp[v]-ADDITIVE CYCLIC CODES

被引：49

作者：

Diao, Lingyu ^{[1
]}

Gao, Jian ^{[1
,2
,3
]}

Lu, Jiyong ^{[4
]}

机构：

[1] Shandong Univ Technol, Sch Math & Stat, Zibo 255000, Peoples R China

[2] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China

[3] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Peoples R China

[4] Tianjin Univ Sci & Technol, Coll Sci, Tianjin 300071, Peoples R China

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2020年 / 14卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Additive cyclic codes; minimal generating sets; dual codes; quantum codes; QUANTUM CODES;

D O I：

10.3934/amc.2020029

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

ZpZp[v]ZpZp[v]-Additive cyclic codes of length (alpha, beta) can be viewed as R[x]-submodules of Z(p)[x]/(x(alpha)-1)xR[x]/(x(beta)-1)Z(p)[x]/(x(alpha)-1)xR[x]/(x beta-1), where R=Z(p)+vZpR=Zp+vZp with v(2)-v. In this paper, we determine the generator polynomials and the minimal generating sets of this family of codes as R[x]R[x]-submodules of Z(p)[x]/(xa-1)xR[x]/(x beta-1)Zp[x]/(xa-1)xR[x]/(x beta-1). We also determine the generator polynomials of the dual codes of Z(p)Z(p)[v]Z(p)Z(p)[v]-additive cyclic codes. Some optimal ZpZp[v]ZpZp[v]-linear codes and MDSS codes are obtained from Z(p)Z(p)[v]Z(p)Z(p)[v]-additive cyclic codes. Moreover, we also get some quantum codes from ZpZp[v]ZpZp[v]-additive cyclic codes.

引用

页码：555 / 572

页数：18

共 22 条

[1]

Abualrub T., 2014, P INT MULT ENG COMP, VII

[2] Z2Z4-Additive Cyclic Codes [J].

Abualrub, Taher ;

Siap, Irfan ;

Aydin, Nuh .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2014, 60 (03) :1508-1514

[3]

Ashraf M., 2015, INT J INF CODING THE, V3, P137

[4] Z2Z2[u]-Cyclic and Constacyclic Codes [J].

Aydogdu, Ismail ;

Abualrub, Taher ;

Siap, Irfan .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2017, 63 (08) :4883-4893

[5] On Zpr Zps-additive codes [J].

Aydogdu, Ismail ;

Siap, Irfan .

LINEAR & MULTILINEAR ALGEBRA, 2015, 63 (10) :2089-2102

[6]

Aydogdu I, 2015, INT J COMPUT MATH, V92, P1806, DOI 10.1080/00207160.2013.859854

[7]

Borges J, 2010, DESIGN CODE CRYPTOGR, V54, P167, DOI 10.1007/s10623-009-9316-9

[8] Z2Z4-Additive Cyclic Codes, Generator Polynomials, and Dual Codes [J].

Borges, Joaquim ;

Fernandez-Cordoba, Cristina ;

Ten-Valls, Roger .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2016, 62 (11) :6348-6354

[9] Quantum error correction via codes over GF (4) [J].

Calderbank, AR ;

Rains, EM ;

Shor, PW ;

Sloane, NJA .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1998, 44 (04) :1369-1387

[10] Association schemes and coding theory [J].

Delsarte, P ;

Levenshtein, VI .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1998, 44 (06) :2477-2504

← 1 2 3 →