Infinite families of $2$-designs from a class of non-binary Kasami cyclic codes
Abstract
Combinatorial -designs have been an important research subject for many years, as they have wide applications in coding theory, cryptography, communications and statistics. The interplay between coding theory and -designs has been attracted a lot of attention for both directions. It is well known that a linear code over any finite field can be derived from the incidence matrix of a -design, meanwhile, that the supports of all codewords with a fixed weight in a code also may hold a -design. In this paper, by determining the weight distribution of a class of linear codes derived from non-binary Kasami cyclic codes, we obtain infinite families of -designs from the supports of all codewords with a fixed weight in these codes, and calculate their parameters explicitly.
Cite
@article{arxiv.1912.04745,
title = {Infinite families of $2$-designs from a class of non-binary Kasami cyclic codes},
author = {Rong Wang and Xiaoni Du and Cuiling Fan},
journal= {arXiv preprint arXiv:1912.04745},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1903.07459, arXiv:1904.04242