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

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

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 impl...

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Veröffentlicht in:Mathematics (Basel) 2024-01, Vol.12 (2), p.328
Hauptverfasser: Bouyuklieva, Stefka, Bouyukliev, Iliya
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Algorithms
canonical form
Classification
code equivalence
Codes
Equivalence
Fields (mathematics)
graph isomorphism problem
Isomorphism
linear code
Linear codes
Orbits
Software
Study and teaching
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Zusammenfassung: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 q
ISSN:2227-7390
2227-7390
DOI:10.3390/math12020328