Explicit Full Correlation Distribution of Sequence Families Using Plateaued Functions

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 w...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 64; no. 4; pp. 2858 - 2875
Main Authors: Boztas, Serdar, Ozbudak, Ferruh, Tekin, Eda
Format: Journal Article
Language:English
Published: New York IEEE 01.04.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
algebraic coding theory
algebraic curves over finite fields
Code Division Multiple Access
Correlation
cross-correlation
Cryptography
Electronic mail
Gold
Mathematical model
Multiaccess communication
non-quadratic functions
plateaued functions
Quadratic equations
Sequences
Transforms
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary: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 <inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> and degrees <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> of the Galois field <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{p^{n}} </tex-math></inline-formula> 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.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2017.2789208