Explicit Full Correlation Distribution of Sequence Families Using Plateaued Functions

BOZTAŞ S., ÖZBUDAK F., TEKİN E.

IEEE TRANSACTIONS ON INFORMATION THEORY, cilt.64, sa.4, ss.2858-2875, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 64 Sayı: 4
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1109/tit.2017.2789208
  • Dergi Adı: IEEE TRANSACTIONS ON INFORMATION THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2858-2875
  • Anahtar Kelimeler: Sequences, cross-correlation, algebraic coding theory, algebraic curves over finite fields, plateaued functions, non-quadratic functions, BINARY SEQUENCES, CROSS-CORRELATION, SETS
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

The design of code division multiple access sequence families dates back to the Gold sequences from the 1960s. Since then there has been a number of different such designs with good correlation properties, some optimal and some near-optimal. In this paper, we use the concept of plateaued functions with arbitrary degree, in order to compute their full correlation distributions. First, we give an explicit correlation distribution of a sequence family using a non-quadratic function. Then for the quadratic functions, we present a general classification of "Gold-like" sequence families for all possible characteristics p and degrees n of the Galois field F-pn used to define the sequences. We are able to obtain the full correlation distribution of the families we consider. This paper also uses techniques from the theory of algebraic curves in order to obtain some of the results.