A Family of q-Ary Cyclic Codes with Optimal Parameters

Wenhua ZHANG  Shidong ZHANG  Yong WANG  Jianpeng WANG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.3   pp.631-633
Publication Date: 2020/03/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2019EAL2126
Type of Manuscript: LETTER
Category: Coding Theory
linear code,  cyclic code,  Hamming distance,  minimum distance,  optimal code,  

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The objective of this letter is to present a family of q-ary codes with parameters $[ rac{q^m-1}{q-1}, rac{q^m-1}{q-1}-2m,d]$, where m is a positive integer, q is a power of an odd prime and 4≤d≤5. The parameters are proved to be optimal or almost optimal with respect to an upper bound on linear codes.