Explicit Full Correlation Distribution of Sequence Families Using Plateaued Functions

Date

2018-04-01

Author

BOZTAŞ, Serdar
Özbudak, Ferruh
TEKİN, Eda

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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.

Subject Keywords

Sequences, Cross-correlation, Algebraic coding theory, Algebraic curves over finite fields, Plateaued functions, Non-quadratic functions

URI

https://hdl.handle.net/11511/38631

Journal

IEEE TRANSACTIONS ON INFORMATION THEORY

DOI

https://doi.org/10.1109/tit.2017.2789208

Collections

Department of Mathematics, Article

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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.