Every Fq -linear code is equivalent to a non-trivial multi-twisted code 

Abstract

Aydina and Halilovi\'{c} [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 Sn. 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 to study linear codes. In particular, we can investigate the structure of multi-twisted codes instead of Fq-linear codes. 2000 Mathematics subject classification: 94B15, 16S36.