Weight enumerators of all irreducible cyclic codes of length n

被引：0

作者：

Kumar, Pankaj ^{[1
]}

Riddhi ^{[1
]}

机构：

[1] Guru Jambheshwar Univ Sci & Technol, Dept Math, Hisar 125001, India

来源：

DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS | 2023年 / 15卷 / 08期

关键词：

Irreducible cyclic codes; cyclotomic cosets; weight distribution; DISTRIBUTIONS;

D O I：

10.1142/S1793830922501798

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let n = p1α1p2α2⋯prαrpr+1αr+1⋯pvαv, where p1,p2,⋯,pv are distinct odd primes, be an integer and Fq be a finite field of order q with gcd(q,n) = 1. We determine the weight enumerators of all irreducible cyclic codes of length n over Fq when multiplicative order of q modulo piαi is piβi; 1 ≤ i ≤ r and 2piβi; r + 1 ≤ i ≤ v, where 0 ≤ βi ≤ αi - 1. © 2023 World Scientific Publishing Company.

引用

页数：13

共 15 条

[1] The Weight Distribution of Some Irreducible Cyclic Codes
Ding, Cunsheng
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2009, 55 (03) : 955 - 960
[2] Feng T, 2012, DESIGN CODE CRYPTOGR, V62, P253, DOI 10.1007/s10623-011-9514-0
[3] THE WEIGHT DISTRIBUTIONS OF SOME IRREDUCIBLE CYCLIC CODES OF LENGTH pn AND 2pn
Kumar, Pankaj
Sangwan, Monika
Arora, Suresh Kumar
[J]. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2015, 9 (03) : 277 - 289
[4] A class of five-weight cyclic codes and their weight distribution
Liu, Yan
Yan, Haode
[J]. DESIGNS CODES AND CRYPTOGRAPHY, 2016, 79 (02) : 353 - 366
[5] MacWilliams F. J., 1977, The theory of error-correcting codes. II
[6] Weight distributions of some irreducible cyclic codes of length n
Riddhi
Singh, Kulvir
Kumar, Pankaj
[J]. INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2022, 53 (04) : 1073 - 1082
[7] The weight distributions of irreducible cyclic codes of length 2(n)p(m)
Sangwan, Monika
Kumar, Pankaj
[J]. ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2018, 11 (06)
[8] The weight distributions of irreducible cyclic codes of length 2m
Sharma, Anuradha
Bakshi, Gurmeet K.
Raka, Madhu
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 2007, 13 (04) : 1086 - 1095
[9] A note on weight distributions of irreducible cyclic codes
Sharma, Anuradha
Sharma, Amit K.
[J]. DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2014, 6 (03)
[10] The weight distribution of some irreducible cyclic codes
Sharma, Anuradha
Bakshi, Gurmeet K.
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 2012, 18 (01) : 144 - 159

← 1 2 →