2024/01/26 by Yuqing Fu, Hongwei Liu, Fu, Yuqing +1
Computer Science · Engineering · #Coding theory and cryptography #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2401.14663
openalex publication_date 2024/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
BCH codes form an important subclass of cyclic codes, and are widely used in compact discs, digital audio tapes and other data storage systems to improve data reliability. As far as we know, there are few results on q-ary BCH codes of length n=\fracqm+1q+1. This is because it is harder to deal with BCH codes of such length. In this paper, we study q-ary BCH codes with lengths n=\fracqm+1q+1 and n=qm+1. These two classes of BCH codes are always LCD codes. For n=\fracqm+1q+1, the dimensions of narrow-sense BCH codes of length n with designed distance δ=ℓ q(m-1)/(2)+1 are determined, where q>2 and 2≤ ℓ ≤ q-1. Moreover, the largest coset leader is given for m=3 and the first two largest coset leaders are given for q=2. The parameters of BCH codes related to the first few largest coset leaders are investigated. Some binary BCH codes of length n=(2m+1)/(3) have optimal parameters. For ternary narrow-sense BCH codes of length n=3m+1, a lower bound on the minimum distance of their dual codes is developed, which is good in some cases.