The Proof of Lin’s Conjecture via the Decimation-Hadamard Transform
Honggang Hu, Shuai Shao, Guang Gong, Tor Helleseth · IEEE Transactions on Information Theory · 2014
In 1998, Lin presented a conjecture on a class of ternary sequences with ideal two-level autocorrelation. 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 Teichmüller character, and combinatorial techniques for enumerating the Hamming weights of ternary numbers. As a by-product, we also prove that the ternary sequences conjectured by Lin are Hadamard equivalent to ternary m-sequences.