Primitive idempotents and generator polynomials of some minimal cyclic codes of length \({p^n}{q^m}\)
type: Item
instance of: scholarly article
title: Primitive idempotents and generator polynomials of some minimal cyclic codes of length \({p^n}{q^m}\)
zbMATH Open document ID: 1358.94097
DOI: 10.1504/IJICOT.2014.066087
author: Pankaj Kumar
author: Sudhir Batra
author: Suresh Kumar Arora
published in: International Journal of Information and Coding Theory
publication date: 2015-11-03T00:00:00Z
review text: Summary: Let \(p, q\) and \(l\) be distinct odd primes such that \(l\) is a primitive root modulo \(p^n\) as well as modulo \(q^m\) with \(\gcd(\varphi(p),\varphi(q)) = 2\). Then the explicit expressions for the complete set of \(2mn + m + n + 1\) primitive idempotents of the minimal cyclic codes of length \({p^n}{q^m}\) over \(\mathrm{GF}(l)\) are obtained. An algorithm is also given to factorise the polynomial \((x^n - 1)\) over \(\mathrm{GF}(k)\), where \(n\) is an integer such that \(\gcd(n, k) = 1\). Using the algorithm generator polynomials of the above minimal cyclic codes can be computed numerically. Some bounds on the minimum distance of these minimal cyclic codes are also obtained.
Mathematics Subject Classification ID: 94B15
zbMATH DE Number: 6503839
zbMATH Keywords: cyclotomic cosets
zbMATH Keywords: primitive idempotents
zbMATH Keywords: generator polynomials
zbMATH Keywords: cyclic codes
zbMATH Keywords: minimum distance
MaRDI profile type: Publication
full work available at URL: ijicot.2014.066087
OpenAlex ID: W1977410632
Recommended article: Idempotents Generators for Minimal Cyclic Codes of Length p n q
Recommended article: Q4609233
Recommended article: Primitive idempotents of irreducible cyclic codes of length \(p^nq^m\)
Recommended article: Q3095921
Recommended article: Primitive idempotents of irreducible cyclic codes of length \(n\)
Recommended article: Primitive idempotents of cyclic codes of length \(p\) and 2\(p\)
Recommended article: Minimum distance and idempotent generators of minimal cyclic codes of length ${p_1}^{\alpha_1}{p_2}^{\alpha_2}{p_3}^{\alpha_3}$
Recommended article: Primitive idempotents of irreducible cyclic codes and self-dual cyclic codes over Galois rings
Recommended article: Primitive Idempotents and Constacyclic Codes over Finite Chain Rings
Recommended article: Q4571123
description: scientific article; zbMATH DE number 6503839