New families of SOD and LCD codes, and LRCs based on plateaued functions
Computational and Applied Mathematics, cilt.46, sa.2, 2027 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 46 Sayı: 2
- Basım Tarihi: 2027
- Doi Numarası: 10.1007/s40314-026-03920-0
- Dergi Adı: Computational and Applied Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Compendex, zbMATH, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: Divisible code, LCD code, Linear code, LRC, Self-orthogonal code, Weakly regular plateaued function
- Akdeniz Üniversitesi Adresli: Evet
Özet
A linear code is said to be self-orthogonal if it is a subset of its dual code. Such codes play an important role in coding theory, with notable application in the construction of Linear Complementary Dual (LCD) codes. Recent studies have explored the construction of self-orthogonal codes from functions over finite fields. In this paper, we apply the augmentation method to obtain new families of few-weight linear codes derived from weakly regular plateaued unbalanced functions over finite fields of odd characteristics. The constructed codes are shown to be self-orthogonal and divisible (SOD) codes under specific conditions. We also observe that some constructed codes are Locally Recoverable Codes (LRCs) with locality 2. Furthermore, we show how the obtained SOD codes can be utilised to generate new infinite families of LCD codes. As a result, we construct new families of p-ary SOD codes (especially, LRCs) and LCD codes, and in certain instances we achieve (almost) optimal codes.