A Comparison of Distance Bounds for Quasi-Twisted Codes

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Ezerman M. F., Lampos J. M., Ling S., Ozkaya B., Tharnnukhroh J.

IEEE TRANSACTIONS ON INFORMATION THEORY, cilt.67, sa.10, ss.6476-6490, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 67 Sayı: 10
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1109/tit.2021.3084146
  • 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.6476-6490
  • Anahtar Kelimeler: Eigenvalues and eigenfunctions, Manganese, Spectral analysis, Scholarships, Indexes, Generators, Product codes, Quasi-twisted code, concatenated code, minimum distance bound, polynomial matrices, spectral analysis, MINIMUM DISTANCE
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

Spectral bounds on the minimum distance of quasi-twisted codes over finite fields are proposed, based on eigenvalues of polynomial matrices and the corresponding eigenspaces. They generalize the Semenov-Trifonov and Zeh-Ling bounds in a way similar to how the Roos and shift bounds extend the BCH and HT bounds for cyclic codes. The eigencodes of a quasi-twisted code in the spectral theory and the outer codes in its concatenated structure are related. A comparison based on this relation verifies that the Jensen bound always outperforms the spectral bound under special conditions, which yields a similar relation between the Lally and the spectral bounds. The performances of the Lally, Jensen and spectral bounds are presented in comparison with each other.