CORRELATION DISTRIBUTION OF A SEQUENCE FAMILY GENERALIZING SOME SEQUENCES OF TRACHTENBERG


ÖZBUDAK F. , Tekin E.

ADVANCES IN MATHEMATICS OF COMMUNICATIONS, vol.15, no.4, pp.647-662, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.3934/amc.2020087
  • Title of Journal : ADVANCES IN MATHEMATICS OF COMMUNICATIONS
  • Page Numbers: pp.647-662
  • Keywords: Sequences, cross-correlation, plateaued functions, BINARY SEQUENCES

Abstract

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)}.