On the parameters of extended primitive cyclic codes and the related designs
Information Theory
2023-06-16 v2 math.IT
Abstract
Very recently, Heng et al. studied a family of extended primitive cyclic codes. It was shown that the supports of all codewords with any fixed nonzero Hamming weight of this code supporting 2-designs. In this paper, we study this family of extended primitive cyclic codes in more details. The weight distribution is determined. The parameters of the related -designs are also given. Moreover, we prove that the codewords with minimum Hamming weight supporting 3-designs, which gives an affirmative solution to Heng's conjecture.
Cite
@article{arxiv.2306.07718,
title = {On the parameters of extended primitive cyclic codes and the related designs},
author = {Haode Yan and Yanan Yin},
journal= {arXiv preprint arXiv:2306.07718},
year = {2023}
}