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The Proof of Lin’s Conjecture via the Decimation-Hadamard Transform.
- Source :
-
IEEE Transactions on Information Theory . Aug2014, Vol. 60 Issue 8, p5054-5064. 11p. - Publication Year :
- 2014
-
Abstract
- 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. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 60
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 97068632
- Full Text :
- https://doi.org/10.1109/TIT.2014.2327625