More results on hulls of some primitive binary and ternary BCH codes

作者：Lei, Yinzhao; Li, Chengju^*; Wu, Yansheng; Zeng, Peng

来源：Finite Fields and their Applications, 2022, 82: 102066.

DOI：10.1016/j.ffa.2022.102066

• BCH code
• Cyclic code
• Self-orthogonal code
• Hull
• Cyclotomic coset

The (Euclidean) hull of a linear code is defined to be the intersection of the code and its Euclidean dual. It is clear that the hulls are self-orthogonal codes, which are an important type of linear codes due to their wide applications in communication and cryptography. Let C be an [n, k] cyclic code over Fq, where Fq is the finite field of order q. In this paper, we will employ the defining set of the code C to present a general characterization when its hull has dimension k - t. Furthermore, we mainly focus on the primitive q-ary BCH codes C(q,n,delta,b) when b = 0 and b = 1 based on the general characterization. Especially for binary and ternary cases, we will present several sufficient and necessary conditions that the hulls of the codes C(q,n,delta,b) have dimensions k-2 and k-3 by giving lower and upper bounds on their designed distances, which extends the results of [17]. In addition, several classes of binary and ternary self-orthogonal codes are proposed via the hulls of BCH codes and their parameters are investigated in some special cases.

• 单位
  南京邮电大学