Codes from the Skew Ring ... - ...
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Tarih
2023
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
American Mathematical Society
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In this work, we study codes generated by elements in the skew group matrix ring M k ( R ) ? ? G M_k(R)\rtimes _{\varphi }G , where R R is a finite commutative Frobenius ring, G G is an arbitrary finite group, and ? \varphi is a group homomorphism from G G to A u t ( M k ( R ) ) Aut(M_k(R)) . We then determine all possible group homomorphisms ? : G ? A u t ( M 2 ( F 2 ) ) , \varphi : G \rightarrow Aut(M_2(\mathbb {F}_2)), for the cases where G G is a cyclic group and a dihedral group. Finally, by using skew generator matrices we provide examples of binary self-dual codes and also binary linear optimal codes.
Açıklama
Anahtar Kelimeler
skew codes, optimal codes, G-codes, self-dual codes
Kaynak
Algebra and Coding Theory
WoS Q Değeri
Scopus Q Değeri
Cilt
785
Sayı
Künye
Dougherty, S. T., Sahinkaya, S. ve Üstün, D. (2023). Codes from the Skew Ring ... - .... Contemporary Mathematics, 785. Doi: 10.1090/conm/785/15778
