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A Family of at Least Almost Optimal p-Ary Cyclic Codes Xia LI Deng TANG Feng CHENG Publication 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 Keyword: cyclic code, linear code, Hamming distance, minimal distance, Full Text: PDF(115.2KB)>>
Summary: 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. | ||||||||||
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