منابع مشابه
Classifying cocyclic Butson Hadamard matrices
We classify all the cocyclic Butson Hadamard matrices BH(n, p) of order n over the pth roots of unity for an odd prime p and np ≤ 100. That is, we compile a list of matrices such that any cocyclic BH(n, p) for these n, p is equivalent to exactly one element in the list. Our approach encompasses non-existence results and computational machinery for Butson and generalized Hadamard matrices that a...
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We study the circulant complex Hadamard matrices of order n whose entries are l-th roots of unity. For n = l prime we prove that the only such matrix, up to equivalence, is the Fourier matrix, while for n = p+ q, l = pq with p, q distinct primes there is no such matrix. We then provide a list of equivalence classes of such matrices, for small values of n, l.
متن کاملButson Hadamard matrices with partially cyclic core
In this paper, we introduce a class of generalized Hadamard matrices, called a Butson Hadamard matrix with partially cyclic core. Then a new construction method for Butson Hadamard matrices with partially cyclic core is proposed. The proposed matrices are constructed from the optimal balanced low-correlation zone(LCZ) sequence set which has correlation value −1 within LCZ.
متن کاملCocyclic Butson Hadamard matrices and Codes over Zn via the Trace Map
Over the past couple of years trace maps over Galois fields and Galois rings have been used very successfully to construct cocyclic Hadamard, complex Hadamard and Butson Hadamard matrices and subsequently to generate simplex codes over Z4,Z2s and Zp and new linear codes over Zps . Here we define a new map, the trace-like map and more generally the weighted-trace map and extend these techniques ...
متن کاملCounting Results for Thin Butson Matrices
A partial Butson matrix is a matrix H ∈ MM×N (Zq) having its rows pairwise orthogonal, where Zq ⊂ C× is the group of q-th roots of unity. We investigate here the counting problem for these matrices in the “thin” regime, where M = 2, 3, . . . is small, and where N → ∞ (subject to the condition N ∈ pN when q = pk > 2). The proofs are inspired from the de Launey-Levin and Richmond-Shallit counting...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2018
ISSN: 0012-365X
DOI: 10.1016/j.disc.2018.05.012