Linear codes of 2-designs associated with subcodes of the ternary generalized Reed-Muller codes
Information Theory
2019-07-31 v1 math.IT
Abstract
In this paper, the 3-rank of the incidence matrices of 2-designs supported by the minimum weight codewords in a family of ternary linear codes considered in [C. Ding, C. Li, Infinite families of 2-designs and 3-designs from linear codes, Discrete Mathematics 340(10) (2017) 2415--2431] are computed. A lower bound on the minimum distance of the ternary codes spanned by the incidence matrices of these designs is derived, and it is proved that the codes are subcodes of the 4th order generalized Reed-Muller codes.
Keywords
Cite
@article{arxiv.1907.13032,
title = {Linear codes of 2-designs associated with subcodes of the ternary generalized Reed-Muller codes},
author = {Cunsheng Ding and Chunming Tang and Vladimir D. Tonchev},
journal= {arXiv preprint arXiv:1907.13032},
year = {2019}
}