Dihedral Group Codes Over Finite Fields

Dihedral Group Codes Over Finite Fields

Bazzi and Mitter showed that binary dihedral group codes are asymptotically good. In this paper we prove that the dihedral group codes over any finite field with strong duality property are asymptotically good. If the characteristic of the field is even, self-dual dihedral group codes are asymptotic...

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Veröffentlicht in:IEEE transactions on information theory 2021-08, Vol.67 (8), p.5016-5025
Hauptverfasser: Fan, Yun, Lin, Liren
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Asymptotic properties
asymptotically good
Dihedral group codes
Fans
Fields (mathematics)
finite fields
Indexes
LCD codes
Linear codes
Liquid crystal displays
self-dual codes
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Beschreibung
Zusammenfassung:Bazzi and Mitter showed that binary dihedral group codes are asymptotically good. In this paper we prove that the dihedral group codes over any finite field with strong duality property are asymptotically good. If the characteristic of the field is even, self-dual dihedral group codes are asymptotically good. If the characteristic of the field is odd, maximal self-orthogonal dihedral group codes and LCD dihedral group codes are asymptotically good.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2021.3088457