A correction and improvements of some recent results on walsh transforms of gold type and Kasami-Welch type functions

Coşgun A., ÖZBUDAK F.

6th International Workshop on Arithmetic of Finite Fields, WAIFI 2016, Ghent, Belçika, 13 - 15 Temmuz 2016, ss.243-257 identifier identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası:
  • Doi Numarası: 10.1007/978-3-319-55227-9_17
  • Basıldığı Şehir: Ghent
  • Basıldığı Ülke: Belçika
  • Sayfa Sayıları: ss.243-257
  • Anahtar Kelimeler: Finite fields, Gold type functions, Kasami-Welch type functions, Walsh transform
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We give explicit evaluations of Walsh transforms of Gold type functions f(x) = Tr-K (x(2a +1) + x(2b +1)), 0 <=< a < b when gcd (b - a, k) = gcd (b + a, k) and Kasami-Welch type functions f (x) = Tr-K (2(ta+1)/x(2a +1)), when t is odd, gcd (2(k) - 1,2(a) + 1) = 1, k is even. Therefore we correct a recent result of Roy'2012, we solve an open problem stated in Roy'2012 and we improve and generalize some results of Roy'2012 and Lahtonen-McGuire-Ward'2007.