On complementary dual multinegacirculant codes

Alahmadi, Adel; Guneri, Cem; Ozkaya, BUKET; Shoaib, Hatoon; Sole, Patrick

doi:10.1007/s12095-019-00364-8

On complementary dual multinegacirculant codes

Alahmadi A., Guneri C., Ozkaya B., Shoaib H., Sole P.

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, cilt.12, sa.1, ss.101-113, 2020 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 12 Sayı: 1
Basım Tarihi: 2020
Doi Numarası: 10.1007/s12095-019-00364-8
Dergi Adı: CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, zbMATH
Sayfa Sayıları: ss.101-113
Anahtar Kelimeler: LCD codes, Quasi-twisted codes, Gilbert-Varshamov bound
Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

Linear codes with complementary duals intersect with their duals trivially. Multinegacirculant codes that are complementary dual are characterized algebraically and some good codes are found in this family. Exact enumeration is performed for indices 2 and 3, whereas special choices of the co-index and base field size are needed for higher indices. Asymptotic existence results are derived for the special class of such codes that have co-index a power of two by means of Dickson polynomials. This shows that there are infinite families of complementary dual multinegacirculant codes with relative distance satisfying a modified Gilbert-Varshamov bound.