2018/02/15 by Ronald Orozco López, López, Ronald Orozco · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Finite Group Theory Research #graph theory and CDMA systems #math.CO #math.GR
paper · pdf · doi:10.48550/arxiv.1802.05788
23 pages
arxiv created 2019/04/11 · arxiv updated 2019/04/12
In this paper a variety of issues are discussed, Schur ring, S-sets, circulant orbits, decimation operator and Hadamard matrices and their relation between them is shown. Firstly we define the complete S-sets. Next, we study the structure of Schur ring with circulant basic sets over \Z2n and we define the free and non-free circulant S-sets, the symmetric, non-symmetric and antisymmetric circulant S-sets. We prove that all this S-sets are invariants under decimation. Finally, we prove that if a Hadamard matrix exist then this is contained in a complete S-set. Also, we prove that can't exist circulant and with one core Hadamard matrices with some particular structure. These theorems include a result known on symmetric circulant Hadamard matrices of order 4n only when n is an odd number.