Self-dual codes from Paley-type bipartite graphs defined by quartic residues
Applicable Algebra in Engineering, Communications and Computing, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s00200-026-00757-2
- Dergi Adı: Applicable Algebra in Engineering, Communications 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)
- Anahtar Kelimeler: Linear codes, Paley-type bipartite graphs, Self-dual codes
- Bilecik Şeyh Edebali Üniversitesi Adresli: Evet
Özet
We prove that the intersection number (Formula presented.) is even for every h∈Fq∗, where S is the subgroup of quartic residues in Fq∗, under the assumptions that q is an odd prime power with q≡5(mod16) and k=4. This resolves Conjecture 9 of [2], where the binary codes Cq,k derived from the neighborhood designs of Paley-type bipartite graphs P(q, k) were studied for an odd prime q; our result also extends the conclusion of that conjecture from odd primes to odd prime powers.