A Family of at Least Almost Optimal p-Ary Cyclic Codes

Xia LI  Deng TANG  Feng CHENG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A    No.9    pp.2048-2051
Publication Date: 2017/09/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E100.A.2048
Type of Manuscript: LETTER
Category: Coding Theory
cyclic code,  linear code,  Hamming distance,  minimal distance,  

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Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms compared with the linear block codes. The objective of this letter is to present a family of p-ary cyclic codes with length $ rac{p^m-1}{p-1}$ and dimension $ rac{p^m-1}{p-1}-2m$, where p is an arbitrary odd prime and m is a positive integer with gcd(p-1,m)=1. The minimal distance d of the proposed cyclic codes are shown to be 4≤d≤5 which is at least almost optimal with respect to some upper bounds on the linear code.