An improvement on the bounds of Weil exponential sums over Gallois rings with some applications

Ling S., Ozbudak F.

IEEE TRANSACTIONS ON INFORMATION THEORY, cilt.50, sa.10, ss.2529-2539, 2004 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 50 Sayı: 10
  • Basım Tarihi: 2004
  • Doi Numarası: 10.1109/tit.2004.834743
  • Dergi Adı: IEEE TRANSACTIONS ON INFORMATION THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2529-2539
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We present an upper bound for Weil-type exponential sums over Galois rings of characteristic p(2) which improves on the analog of the Weil-Carlitz-Uchiyama bound for Galois rings obtained by Kumar, Helleseth, and Calderbank. A more refined bound, expressed in terms of genera of function fields, and an analog of McEliece's theorem on the divisibility of the homogeneous weights of codewords in trace codes over Z(p)2, are also derived. These results lead to an improvement on the estimation of the minimum distance of certain trace codes over Z(p)2 and the bounds on the correlation of certain nonlinear p-ary sequences.