Infinite families of 2-designs and 3-designs from linear codes
Information Theory
2017-06-02 v1 Combinatorics
math.IT
Abstract
The interplay between coding theory and -designs started many years ago. While every -design yields a linear code over every finite field, the largest for which an infinite family of -designs is derived directly from a linear or nonlinear code is . Sporadic -designs and -designs were derived from some linear codes of certain parameters. The major objective of this paper is to construct many infinite families of -designs and -designs from linear codes. The parameters of some known -designs are also derived. In addition, many conjectured infinite families of -designs are also presented.
Cite
@article{arxiv.1607.04813,
title = {Infinite families of 2-designs and 3-designs from linear codes},
author = {Cunsheng Ding and Chengju Li},
journal= {arXiv preprint arXiv:1607.04813},
year = {2017}
}