Additive complementary dual codes from group characters
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Tarih
2022
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Institute of Electrical and Electronics Engineers (IEEE)
Erişim Hakkı
info:eu-repo/semantics/restrictedAccess
Özet
Additive codes have become an increasingly important topic in algebraic coding theory due to their applications in quantum error-correction and quantum computing. Linear Complementary Dual (LCD) codes play an important role for improving the security of information against certain attacks. Motivated by these facts, we define additive complementary dual codes (ACD for short) over a finite abelian group in terms of an arbitrary duality on the ambient space and examine their properties. We show that the best minimum weight of ACD codes is always greater than or equal to the best minimum weight of LCD codes of the same size and that this inequality is often strict. We give some matrix constructions for quaternary ACD codes from a given quaternary ACD code and also from a given binary self-orthogonal code. Moreover, we construct an algorithm to determine if a given quaternary additive code is an ACD code with respect to all possible symmetric dualities. We also determine the largest minimum distance of quaternary ACD codes for lengths n <= 10. The obtained codes are either optimal or near optimal according to Bierbrauer et al+. (2009).
Açıklama
Anahtar Kelimeler
LCD codes, additive codes, optimal codes
Kaynak
IEEE Transactions on Information Theory
WoS Q Değeri
Q2
Scopus Q Değeri
Q1
Cilt
68
Sayı
7
Künye
Dougherty, S. T., Şahinkaya, S. ve Üstün, D. (2022). Additive Complementary Dual Codes From Group Characters, IEEE Transactions on Information Theory, 68 (7), 4444-4452. Doi: 10.1109/TIT.2022.3162181
