A new family of linear maximum rank distance codes
John Sheekey
TL;DR
This paper introduces a new family of linear maximum rank distance codes that generalize Gabidulin codes, include inequivalent codes, and relate to semifields, expanding the landscape of MRD code constructions.
Contribution
It constructs a new family of MRD codes for all parameters, extending known families and analyzing their automorphism groups.
Findings
Contains the only known family of MRD codes for general parameters
Includes codes inequivalent to Gabidulin codes
Calculates automorphism groups of these codes
Abstract
In this article we construct a new family of linear maximum rank distance (MRD) codes for all parameters. This family contains the only known family for general parameters, the Gabidulin codes, and contains codes inequivalent to the Gabidulin codes. This family also contains the well-known family of semifields known as Generalised Twisted Fields. We also calculate the automorphism group of these codes, including the automorphism group of the Gabidulin codes.
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