CORRELATION DISTRIBUTION OF A SEQUENCE FAMILY GENERALIZING SOME SEQUENCES OF TRACHTENBERG

ÖZBUDAK F., Tekin E.

ADVANCES IN MATHEMATICS OF COMMUNICATIONS, cilt.15, sa.4, ss.647-662, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 4
  • Basım Tarihi: 2021
  • Doi Numarası: 10.3934/amc.2020087
  • Dergi Adı: ADVANCES IN MATHEMATICS OF COMMUNICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.647-662
  • Anahtar Kelimeler: Sequences, cross-correlation, plateaued functions, BINARY SEQUENCES
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we give a classification of a sequence family, over arbitrary characteristic, adding linear trace terms to the function g(x) = Tr(x(d)), where d = p(2k) - p(k) + 1, first introduced by Trachtenberg. The family has p(n) + 1 cyclically distinct sequences with period p(n) - 1. We compute the exact correlation distribution of the function g(x) with linear m-sequences and amongst themselves. The cross-correlation values are obtained as C-i,C-j(tau) is an element of {-1, -1 +/- p(n+e/2), -1 + p(n)}.