ON CYCLIC AND NEGACYCLIC CODES WITH ONE-DIMENSIONAL HULLS AND THEIR APPLICATIONS
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Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Amer Inst Mathematical Sciences-Aims
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Linear codes over finite fields with small dimensional hulls have received much attention due to their applications in cryptology and quantum computing. In this paper, we study cyclic and negacyclic codes with onedimensional hulls. We determine precisely when cyclic and negacyclic codes over finite fields with one-dimensional hulls exist. We also introduce onedimensional linear complementary pairs of cyclic and negacyclic codes. As an application, we obtain numerous optimal or near optimal cyclic codes with onedimensional hulls over different fields and, by using these codes, we present new entanglement-assisted quantum error-correcting codes (EAQECCs). In particular, some of these EAQEC codes are maximal distance separable (MDS). We also obtain one-dimensional linear complementary pairs of cyclic codes, which are either optimal or near optimal.
Açıklama
Anahtar Kelimeler
Assisted Quantum Codes, Algebraic Structure, Linear Codes, Permutation
Kaynak
Advances in Mathematics of Communications
WoS Q Değeri
Q3
Scopus Q Değeri
Q1
Cilt
18
Sayı
5
