On additive codes with one-rank hulls

Dougherty S., Şahinkaya S., Ustun D.

Applicable Algebra in Engineering, Communications and Computing, cilt.36, sa.6, ss.1237-1252, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 6
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s00200-024-00663-5
  • Dergi Adı: Applicable Algebra in Engineering, Communications and Computing
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1237-1252
  • Anahtar Kelimeler: Additive codes, Duality, Hull of a code
  • Ankara Üniversitesi Adresli: Hayır

Özet

We study additive codes with 1-rank hulls and examine their properties for various dualities of the finite field of order 4. We give several constructions of additive and linear codes with 1-rank hulls. We also relate these codes to additive complementary dual codes (ACD). We give an interesting non-existence result for additive codes with a 1-rank hull for the duality M2 in terms of the parity of the number of generators. We conclude by giving substantive computations finding codes with one-rank hulls for small lengths using our results.