MDS multi-twisted Reed-Solomon codes with small dimensional hull
Harshdeep Singh, Kapish Chand Meena

TL;DR
This paper characterizes conditions for multi-twisted Reed-Solomon codes to be MDS, introduces a new class with specific twists, and explores their hull properties over finite fields.
Contribution
It provides a necessary and sufficient condition for MDS multi-twisted Reed-Solomon codes and introduces a new class with explicit examples and enumeration.
Findings
New class of MDS double-twisted Reed-Solomon codes over finite fields.
Necessary conditions for codes with small hull dimension.
Existence conditions for MDS codes with small hulls.
Abstract
In this paper, we find a necessary and sufficient condition for multi-twisted Reed-Solomon codes to be MDS. In particular, we introduce a new class of MDS double-twisted Reed-Solomon codes with twists and hooks over the finite field , providing a non-trivial example over and enumeration over the finite fields of size up to 17. Moreover, we obtain necessary conditions for the existence of multi-twisted Reed-Solomon codes with small dimensional hull. Consequently, we derive conditions for the existence of MDS multi-twisted Reed-Solomon codes with small dimensional hull.
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Taxonomy
TopicsCoding theory and cryptography · Islamic Finance and Communication · Educational Methods and Media Use
