2013/07/03 by Honggang Hu, Shuai Shao, Hu, Honggang +5
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics #Computer science #Conjecture #Discrete mathematics #FOS: Computer and information sciences #Hadamard transform #Information Theory (cs.IT) #Mathematical analysis #Mathematics #Monomial #Product (mathematics) #Simple (philosophy) #TRACE (psycholinguistics) #Ternary operation #cs.IT #graph theory and CDMA systems #math.IT
paper · pdf · doi:10.48550/arxiv.1307.0885
arxiv created 2013/07/03 · openalex publication_date 2013/07/03 · arxiv updated 2013/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 Teichmüller 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 m-sequences.