Quadratic residue codes over F-p + nu F-p and their Gray images

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Kaya A., Yildiz B., Siap I.

JOURNAL OF PURE AND APPLIED ALGEBRA, cilt.218, sa.11, ss.1999-2011, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 218 Sayı: 11
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1016/j.jpaa.2014.03.002
  • Dergi Adı: JOURNAL OF PURE AND APPLIED ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1999-2011
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this paper quadratic residue codes over the ring F-p + vF(p) are introduced in terms of their idempotent generators. The structure of these codes is studied and it is observed that these codes enjoy similar properties as quadratic residue codes over finite fields. For the case p = 2, Euclidean and Hermitian self-dual families of codes as extended quadratic residue codes are considered and two optimal Hermitian self-dual codes are obtained as examples. Moreover, a substantial number of good p-ary codes are obtained as images of quadratic residue codes over F-p + vF(p) in the cases where p is an odd prime. These results are presented in tables. (C) 2014 Elsevier B.V. All rights reserved.