Explicit Full Correlation Distribution of Sequence Families Using Plateaued Functions

BOZTAŞ, Serdar
Özbudak, Ferruh
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.


Classification of a Sequence Family Using Plateaued Functions
BOZTAŞ, Serdar; Özbudak, Ferruh; Tekin, Eda (2017-06-30)
The design of CDMA sequence families using quadratic functions dates hack 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 characteristi...
On Fibre Products of Kummer Curves with Many Rational Points over Finite Fields
Özbudak, Ferruh; YAYLA, OĞUZ (2014-09-18)
We determined the number of rational points of fibre products of two Kummer covers over a rational point of the projective line in a recent work of F. Ozbudak and B. G. Temur (Des Codes Cryptogr 70(3): 385-404, 2014), where we also constructed explicit examples, including a record and two new entries for the current Table of Curves with Many Points (manYPoints: Table of curves with many points. http://www.manypoints.org (2014). Accessed 30 Sep 2014). Using the methods given in Ozbudak and Gulmez Temur (Des ...
On multiplication in finite fields
Cenk, Murat; Özbudak, Ferruh (2010-04-01)
We present a method for multiplication in finite fields which gives multiplication algorithms with improved or best known bilinear complexities for certain finite fields. Our method generalizes some earlier methods and combines them with the recently introduced complexity notion (M) over cap (q)(l), which denotes the minimum number of multiplications needed in F-q in order to obtain the coefficients of the product of two arbitrary l-term polynomials modulo x(l) in F-q[x]. We study our method for the finite ...
Correlation distribution of a sequence family generalizing some sequences of trachtenberg
Özbudak, Ferruh (2021-08-01)
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)}.
Efficient multiplications in F(5)5n and F(7)7n
Cenk, Murat; Özbudak, Ferruh (2011-08-15)
Efficient multiplications in finite fields of characteristics 5 and 7 are used for computing the Eta pairing over divisor class groups of the hyperelliptic curves Lee et al. (2008) [1]. In this paper, using the recent methods for multiplication in finite fields, the explicit formulas for multiplication in F(5)5n and F(7)7n are obtained with 10 multiplications in F(5)n for F(5)5n and 15 multiplications in F(7)n for F(7)7n improving the results in Cenk and Ozbudak (2008) [4], Cenk et al. (2009) [5], Lee et al...
Citation Formats
S. BOZTAŞ, F. Özbudak, and E. TEKİN, “Explicit Full Correlation Distribution of Sequence Families Using Plateaued Functions,” IEEE TRANSACTIONS ON INFORMATION THEORY, pp. 2858–2875, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38631.