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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 1/2016

01-10-2016

Two classes of cyclic codes and their weight enumerator

Authors: Haode Yan, Chunlei Liu

Published in: Designs, Codes and Cryptography | Issue 1/2016

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Abstract

Let p be an odd prime, and m, k and d be positive integers such that \(2 \le k\le \frac{m+1}{2}\) and \(\hbox {gcd}(m,d)=1. \pi \) is a primitive element of the finite field \({\mathbb {F}}_{p^{m}}\). The weight enumerator of cyclic codes over \({\mathbb {F}}_{p}\) whose duals have 2k zeros \(\pi ^{-(p^{jd}+1)/2}\) and \(-\pi ^{-(p^{jd}+1)/2} (j=0,1,\ldots ,k-1)\) is determined in the present paper. The weight enumerator of cyclic codes over \({\mathbb {F}}_{p}\) whose duals have \(2k-1\) zeros \(\pi ^{-(p^{(k-1)d}+1)/2}, \pi ^{-(p^{jd}+1)/2}\) and \(-\pi ^{-(p^{jd}+1)/2} (j=0,1,\ldots ,k-2)\) is also determined when \(2\not \mid \frac{m}{gcd(m,k-1)}\) holds.
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Metadata
Title
Two classes of cyclic codes and their weight enumerator
Authors
Haode Yan
Chunlei Liu
Publication date
01-10-2016
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 1/2016
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-015-0125-z

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