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 Fpnused 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.

The design of CDMA sequence families using quadratic functions dates back to Gold sequences from the 1960s. Since then there have been a number of different such designs with good correlation properties, some optimal and some near-optimal, and the term “Gold-like” is usually used to denote such sequences. In this paper we use the concept of plateaued functions, not necessarily quadratic, in order to classify such sequence families and present some examples in this direction which depend on the characteristic p and degree n of the Galois field Fpnused to define the sequences.

In this paper we generalize a previous construction in order to design perfect autocorrelation sequences over the so-called PSK+ constellation defined by Boztaş and Udaya [2]. We give a number theoretic criterion for the existence of the new sequences with perfect autocorrelation, and discuss some preliminary numerical results on their aperiodic correlations and merit factors.

In this paper a new binary sequence family with 2n+ 1 cyclically distinct sequences each having length 2n- 1 is presented for an even integer n. The correlation distribution of the family is fully determined. The family has six-valued correlation distribution and its maximum correlation magnitude equals 1+2n/2+1.