Computer Classification of Linear Codes

Computer Classification of Linear Codes

Two algorithms for the classification of linear codes over finite fields are presented. One of the algorithms is based on canonical augmentation and the other one on lattice point enumeration. New classification results over fields with 2, 3 and 4 elements are obtained.

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Veröffentlicht in:IEEE transactions on information theory 2021-12, Vol.67 (12), p.7807-7814
Hauptverfasser: Bouyukliev, Iliya, Bouyuklieva, Stefka, Kurz, Sascha
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
canonical augmentation
Classification
Classification algorithms
code equivalence
Codes
Enumeration
Fields (mathematics)
Generators
lattice point enumeration
Lattices
Linear codes
Orbits
Symmetric matrices
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Beschreibung
Zusammenfassung:Two algorithms for the classification of linear codes over finite fields are presented. One of the algorithms is based on canonical augmentation and the other one on lattice point enumeration. New classification results over fields with 2, 3 and 4 elements are obtained.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2021.3114280