Explicit Full Correlation Distribution of Sequence Families Using Plateaued Functions - Boztas, Serdar; Ozbudak, Ferruh; Tekin, Eda (IEEE transactions on information theory, 2018)
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 \mathbb {F}_{p^{n}} 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.