Constacyclic codes over Z2 [u]/⟨u2⟩ x Z2 [u]/⟨u3⟩ and the MacWilliams identities

被引：0

作者：

Sagar, Vidya ^{[1
]}

Yadav, Ankit ^{[1
]}

Sarma, Ritumoni ^{[1
]}

机构：

[1] Indian Inst Technol Delhi, Dept Math, New Delhi 110016, Delhi, India

来源：

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING | 2024年

关键词：

Constacyclic code; Gray map; Quasi-cyclic code; Weight enumerator; MacWilliams identities; LINEAR CODES; CYCLIC CODES; EUCLIDEAN WEIGHTS; RINGS; LEE;

D O I：

10.1007/s00200-024-00662-6

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this article, we deal with additive codes over the Frobenius ring R2R3 := Z(2)[u]/< u(2)> x Z(2)[u]/< u(3)>. First, we study constacyclic codes over R-2 and R-3 and find their generator polynomials. With the help of these generator polynomials, we determine the structure of constacyclic codes over R2R3. We use Gray maps to show that constacyclic codes over R2R3 are essentially binary generalized quasi-cyclic codes. Moreover, we obtain a number of binary codes with good parameters from these R2R3-constacyclic codes. Besides, several weight enumerators are computed, and the corresponding MacWilliams identities are established.

引用

页数：30

共 50 条

[11] On a Class of (δ plus αu2)-Constacyclic Codes over Fq[u] =/⟨u4⟩
Cao, Yuan
Cao, Yonglin
Gao, Jian
[J]. IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2016, E99A (07) : 1438 - 1445
[12] Quark-lepton mass matrices with U(1) x Z2 x Z2' flavor symmetry
Tanimoto, M
[J]. PHYSICS LETTERS B, 1999, 456 (2-4) : 220 - 231
[13] Cyclic codes over Z2 + uZ2 + u2Z2 + ... + uk-1Z2
Al-Ashker, Mohammed
Hamoudeh, Mohammed
[J]. TURKISH JOURNAL OF MATHEMATICS, 2011, 35 (04) : 737 - 749
[14] Numerical study of the stability of U(1) x U(1) x Z2 Dirichlet defects
Yu, RP
Adam, N
Thatcher, MJ
Morgan, MJ
[J]. CLASSICAL AND QUANTUM GRAVITY, 2001, 18 (23) : L163 - L169
[15] ON Z4Z4[u3]-ADDITIVE CONSTACYCLIC CODES
Prakash, Om
Yadav, Shikha
Islam, Habibul
Sole, Patrick
[J]. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2023, 17 (01) : 246 - 261
[16] Quantum Codes from Constacyclic Codes over the Ring Fq[u1, u2]/⟨u12 - u1,u22 - u2, u1u2 - u2u1⟩
Alkenani, Ahmad N.
Ashraf, Mohammad
Mohammad, Ghulam
[J]. MATHEMATICS, 2020, 8 (05)
[17] The homogeneous distance of (1+u2)-constacyclic codes over F2[u]/⟨u3⟩ and its applications
Ding, Jian
Li, Hongju
Lin, Changlu
[J]. JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2022, 68 (01) : 83 - 100
[18] On constacyclic codes over Z4[u] / ⟨u2-1⟩ and their Gray images
Shi, Minjia
Qian, Liqin
Sok, Lin
Aydin, Nuh
Sole, Patrick
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 2017, 45 : 86 - 95
[19] Torsion codes of a α-constacyclic code over Fpm[u]/⟨u3⟩
Hesari, Roghaye Mohammadi
Samei, Karim
[J]. DISCRETE MATHEMATICS, 2024, 347 (06)
[20] On the structure of Z2Z2[u3]-linear and cyclic codes
Aydogdu, Ismail
Siap, Irfan
Ten-Valls, Roger
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 2017, 48 : 241 - 260

← 1 2 3 4 5 →