2019/03/19 by Xiaoni Du, Rong Wang, Du, Xiaoni +5 · 3 citations
Engineering · Computer Science · #graph theory and CDMA systems #Coding theory and cryptography #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1903.08153
Combinatorial t-designs have been an interesting topic in combinatorics for decades. It is a basic fact that the codewords of a fixed weight in a code may hold a t-design. Till now only a small amount of work on constructing t-designs from codes has been done. In this paper, we determine the weight distributions of two classes of cyclic codes: one related to the triple-error correcting binary BCH codes, and the other related to the cyclic codes with parameters satisfying the generalized Kasami case, respectively. We then obtain infinite families of 2-designs from these codes by proving that they are both affine-invariant codes, and explicitly determine their parameters. In particular, the codes derived from the dual of binary BCH codes hold five 3-designs when m=4.