Linear codes of 2-designs associated with subcodes of the ternary generalized Reed–Muller codes
Document Type
Article
Publication Date
12-11-2019
Department
Department of Mathematical Sciences
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 Ding and Li (Discret Math 340(10):2415–2431, 2017) 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.
Publication Title
Designs, Codes and Cryptography
Recommended Citation
Ding, C.,
Tang, C.,
&
Tonchev, V.
(2019).
Linear codes of 2-designs associated with subcodes of the ternary generalized Reed–Muller codes.
Designs, Codes and Cryptography,
88, 625-641.
http://doi.org/10.1007/s10623-019-00701-1
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/1521