The extended code for a class of generalized Roth-Lempel codes and their properties
Information Theory
2025-08-19 v1 math.IT
Abstract
As we all know, many interesting and important codes are obtained by modifying or combining existing codes. In this paper, we focus on generalized Roth-Lempel (in short, GRL) codes and define a class of extended codes, i.e., the extended generalized Roth-Lempel (in short, EGRL) code. And then for a special class of EGRL codes, we give a parity-check matrix and establish a necessary and sufficient condition for the EGRL code or its dual code to be MDS or AMDS, respectively. Finally, we construct a class of NMDS EGRL codes which is the generalization of the constructions given by Han et al. in 2023, and then completely determine its weight distribution.
Cite
@article{arxiv.2508.12302,
title = {The extended code for a class of generalized Roth-Lempel codes and their properties},
author = {Zhonghao Liang and Qunying Liao},
journal= {arXiv preprint arXiv:2508.12302},
year = {2025}
}
Comments
29pages