A Family of at Least Almost Optimal <I>p</I>-Ary Cyclic Codes

Xia LI; Deng TANG; Feng CHENG

doi:10.1587/transfun.E100.A.2048

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

Xia LI, Deng TANG, Feng CHENG

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.9 pp.2048-2051

Publication Date: 2017/09/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E100.A.2048

Type of Manuscript: LETTER

Category: Coding Theory

Authors

Xia LI
  Southwest Jiaotong University,Chinese Academy of Sciences
Deng TANG
  Southwest Jiaotong University
Feng CHENG
  Southwest Jiaotong University

Keyword

cyclic code, linear code, Hamming distance, minimal distance

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Xia LI, Deng TANG, Feng CHENG, "A Family of at Least Almost Optimal p-Ary Cyclic Codes" in IEICE TRANSACTIONS on Fundamentals, vol. E100-A, no. 9, pp. 2048-2051, September 2017, doi: 10.1587/transfun.E100.A.2048.
Abstract: 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.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.2048/_p

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@ARTICLE{e100-a_9_2048,
author={Xia LI, Deng TANG, Feng CHENG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Family of at Least Almost Optimal p-Ary Cyclic Codes},
year={2017},
volume={E100-A},
number={9},
pages={2048-2051},
abstract={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.},
keywords={},
doi={10.1587/transfun.E100.A.2048},
ISSN={1745-1337},
month={September},}

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TY - JOUR
TI - A Family of at Least Almost Optimal p-Ary Cyclic Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2048
EP - 2051
AU - Xia LI
AU - Deng TANG
AU - Feng CHENG
PY - 2017
DO - 10.1587/transfun.E100.A.2048
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2017
AB - 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.
ER -