How to Find the Equivalence Classes in a Set of Linear Codes in Practice?

Abstract

An algorithm for equivalence of linear codes over finite fields is presented. Its main advantage is that it can extract exactly one representative from each equivalence class among a large number of linear codes. It can also be used as a test for isomorphism of binary matrices. The algorithm is implemented in the program LCequivalence, which is designed to obtain the inequivalent codes in a set of linear codes over a finite field with q64 elements. This program is a module of the free software package QextNewEdition for constructing, classifying and studying linear codes.

Keywords

• linear code
• code equivalence
• canonical form
• graph isomorphism problem