Character Values of the Sidelnikov-Lempel-Cohn-Eastman Sequences
Information Theory
2016-02-19 v1 Combinatorics
math.IT
Number Theory
Abstract
Binary sequences with good autocorrelation properties and large linear complexity are useful in stream cipher cryptography. The Sidelnikov-Lempel-Cohn-Eastman (SLCE) sequences have nearly optimal autocorrelation. However, the problem of determining the linear complexity of the SLCE sequences is still open. Our approach is to exploit the fact that character values associated with the SLCE sequences can be expressed in terms of a certain type of Jacobi sum. By making use of known evaluations of Gauss and Jacobi sums in the "pure" and "small index" cases, we are able to obtain new insight into the linear complexity of the SLCE sequences.
Keywords
Cite
@article{arxiv.1602.05888,
title = {Character Values of the Sidelnikov-Lempel-Cohn-Eastman Sequences},
author = {Şaban Alaca and Goldwyn Millar},
journal= {arXiv preprint arXiv:1602.05888},
year = {2016}
}