A Family Of BCH Codes Over F₅

A family of ternary quasi-perfect BCH codes were presented by Danyo Danev and Stefan Dodunekov. These codes are of minimum distance 5 and covering radius 3. In this paper we show that there exist [5s-1/4,5s-1/4-3s,d]5 BCH codes for all odd s≥3 which put ternary extented to quinary. These codes are of minimum distance 5≤d≤8 and covering radius 4. The first member of the family is [31,22,6] 5 code.This paper consists of three chapters, and the main work is organized as followIn the first chapter, a brief survery of coding theory is given, and the main work of this paper is presented. In the second chapter, we give some basic conceptions and theorems of error-correcting codes and BCH codes. In the third chapter, Firstly, a family of quinary BCH codes are defined. Secondly, their range of the minimum distance is determined by using Hamming bound and BCH bound. Thirdly, we prove that their covering radius is equal to 4 and give an example to further analysis in the end.