The equivalent condition for GRL codes to be MDS, AMDS or self-dual

TL;DR

This paper establishes an equivalent condition for generalized Roth-Lempel linear codes and their duals to be non-RS MDS, AMDS, or non-RS self-dual, expanding understanding of their algebraic properties.

Contribution

It provides a new criterion for identifying when these generalized codes or their duals are non-RS MDS, AMDS, or self-dual, which was not previously known.

Findings

Derived an equivalent condition for the codes to be non-RS MDS, AMDS, or self-dual.

Provided examples illustrating the application of the condition.

Enhanced understanding of algebraic properties of generalized Roth-Lempel codes.

Abstract

It's well known that MDS, AMDS or self dual codes have good algebraic properties, and are applied in communication systems, data storage, quantum codes, and so on. In this paper, we focus on a class of generalized Roth-Lempel linear codes which are not not equivalent to linear codes in [21],[22] and give an equivalent condition for them or their dual to be non RS MDS, AMDS or non RS self-dual and some corresponding examples.