The Proof of Lin's Conjecture via the Decimation-Hadamard Transform
Information Theory
2013-07-04 v1 math.IT
Abstract
In 1998, Lin presented a conjecture on a class of ternary sequences with ideal 2-level autocorrelation in his Ph.D thesis. Those sequences have a very simple structure, i.e., their trace representation has two trace monomial terms. In this paper, we present a proof for the conjecture. The mathematical tools employed are the second-order multiplexing decimation-Hadamard transform, Stickelberger's theorem, the Teichm\"{u}ller character, and combinatorial techniques for enumerating the Hamming weights of ternary numbers. As a by-product, we also prove that the Lin conjectured ternary sequences are Hadamard equivalent to ternary -sequences.
Keywords
Cite
@article{arxiv.1307.0885,
title = {The Proof of Lin's Conjecture via the Decimation-Hadamard Transform},
author = {Honggang Hu and Shuai Shao and Guang Gong and Tor Helleseth},
journal= {arXiv preprint arXiv:1307.0885},
year = {2013}
}