Every $ \mathbb{F}_q $-linear code is equivalent to a multi-twisted code

Abstract

Aydina and Halilović (Finite fields Appl. 45 (2017) 96-106) introduced multi-twisted codes and studied some of their basic properties. Let S be a finite commutative Fq-algebra. An Fq-linear code over S of length n is an Fq-submodule of S n . Recently, Mahmoudi et al. (Finite fields Appl. 64 (2020) 101665) studied Fq-linear codes over Fq-algebras. In this paper, we show that every Fq-linear code is equivalent to a multi-twisted (MT) code. This gives us a new point of view in coding theory. In particular, we obtain a rich mathematical structure for linear codes.