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

作者：Li, Xia; Tang, Deng^*; Cheng, Feng

来源：IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2017, E100A(9): 2048-2051.

DOI：10.1587/transfun.E100.A.2048

• cyclic code
• linear code
• Hamming distance
• minimal distance

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 P-m-1/p-1 and dimension Pm-1/p-1 - 2m, where p is an arbitrary odd prime and m is a positive integer wi1 th 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.

• 出版日期2017-9
• 单位中国科学院信息工程研究所; 西南交通大学; 信息安全国家重点实验室