Quasi-Cyclic Perfect Codes in Doob Graphs and Special Partitions of Galois Rings

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Shi M., Li X., Krotov D. S., ÖZBUDAK F.

IEEE Transactions on Information Theory, cilt.69, sa.9, ss.5597-5603, 2023 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 69 Sayı: 9
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1109/tit.2023.3272566
  • Dergi Adı: IEEE Transactions on Information Theory
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, PASCAL, Aerospace Database, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.5597-5603
  • Anahtar Kelimeler: 1â perfect code, Doob graph, galois ring, quasicyclic code
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

The Galois ring GR(4Δ) is the residue ring Z4[x]/(h(x)), where h(x) is a basic primitive polynomial of degree Δ over Z4. For any odd Δ larger than 1, we construct a partition of GR(4Δ)\{0} into 6-subsets of type {a, b,b -ab-b,b-a,b-b, a+b} and 3-subsets of type {c,b-c, 2c} such that the partition is invariant under the multiplication by a nonzero element of the Teichmuller set in GR(4Δ) and, if Δ is not a multiple of 3, under the action of the automorphism group of GR(4Δ). As a corollary, this implies the existence of quasi-cyclic additive 1-perfect codes of index (2Δ b- 1) in D((2Δb-1)(2Δb-2)/6, 2Δb-1) where D(m, n) is the Doob metric scheme on Z2m+n.