Information sets from defining sets in abelian codes

TL;DR

This paper introduces a method to construct information sets for abelian codes using their defining sets, generalizing previous work on binary TDC codes, which aids in understanding code structure and decoding.

Contribution

It presents a new technique to derive information sets from defining sets for all abelian codes, extending Imai's approach for binary TDC codes.

Findings

Provides a general construction method for abelian codes

Extends Imai's technique beyond binary TDC codes

Facilitates better code analysis and decoding strategies

Abstract

We describe a technique to construct a set of check positions (and hence an information set) for every abelian code solely in terms of its defining set. This generalizes that given by Imai in \cite{Imai} in the case of binary TDC codes.