Extended LP bound for LCD codes and new binary and ternary LCD codes
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s00200-025-00716-3
- Dergi Adı: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Compendex, INSPEC, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Engineering Source (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
Extending the methodology of Dougherty et al. (Int J Inf Coding Theory 4: 116-128, 2017) for binary LCD codes, we develop a generalized linear programming (LP) bound applicable to arbitrary q-ary LCD codes. This unified framework enables tight theoretical bounds for both binary and ternary cases. We subsequently compile an extended LP bound tables for binary LCD codes, which expand the previous results, and we introduce the first LP bound table for ternary LCD codes. Furthermore, we generalize several existing results known for LCD codes, leading to the construction of new binary and ternary LCD codes with better parameters. Lastly, we investigate cyclic and quasi-cyclic LCD codes, employing algebraic techniques.