Self-orthogonal generalized twisted Reed-Solomon codes

TL;DR

This paper characterizes when generalized twisted Reed-Solomon codes are self-orthogonal, providing conditions, non-existence results, and constructing new classes of such codes including non-GRS MDS and NMDS codes.

Contribution

It offers a necessary and sufficient condition for self-orthogonality of these codes and constructs new classes, including non-GRS MDS and NMDS codes.

Findings

Derived a condition for self-orthogonality when h+t ≤ k-1

Proved non-existence of self-orthogonal codes under certain conditions

Constructed new classes of self-orthogonal GRS and non-GRS codes

Abstract

In this paper, by calculating the dual code of the Schur square for the standard twisted Reed-Solomon code, we give a sufficient and necessary condition for the generalized twisted Reed-Solomon code with $h+t\le k-1$ to be self-orthogonal, where $k$ is dimension, $h$ is hook and $t$ is twist. And then, we show that there is no self-orthogonal generalized twisted Reed-Solomon code under some conditions. Furthermore, several classes of self-orthogonal generalized twisted Reed-Solomon codes are constructed, and some of these codes are non-GRS self-orthogonal MDS codes or NMDS codes.