Cyclic p-roots of prime length p and related complex Hadamard matrices
نویسنده
چکیده
In this paper it is proved, that for every prime number p, the set of cyclic p-roots in C is finite. Moreover the number of cyclic p-roots counted with multiplicity is equal to ( 2p−2 p−1 ) . In particular, the number of complex circulant Hadamard matrices of size p, with diagonal entries equal to 1, is less than or equal to ( 2p−2 p−1 ) .
منابع مشابه
Small circulant complex Hadamard matrices of Butson type
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 کاملClassifying 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...
متن کاملA note on the existence of BH(19, 6) matrices
In this note we utilize a non-trivial block approach due to M. Petrescu to exhibit a Butson-type complex Hadamard matrix of order 19, composed of sixth roots of unity. 1 A new Butson-type complex Hadamard matrix A complex Hadamard matrix H is an n × n complex matrix with unimodular entries such that HH∗ = nIn, where ∗ denotes the Hermitian adjoint and In is the identity matrix of order n. Throu...
متن کاملNonexistence of Abelian Difference Sets: Lander’s Conjecture for Prime Power Orders
In 1963 Ryser conjectured that there are no circulant Hadamard matrices of order > 4 and no cyclic difference sets whose order is not coprime to the group order. These conjectures are special cases of Lander’s conjecture which asserts that there is no abelian group with a cyclic Sylow p-subgroup containing a difference set of order divisible by p. We verify Lander’s conjecture for all differenc...
متن کاملComplex Golay sequences: structure and applications
Complex Golay sequences were introduced in 1992 to generalize constructions for Hadamard matrices using Golay sequences. (In the last section of this paper we describe some independent earlier work on quadriphase pairs–equivalent objects used in the setting of signal processing.) Since then we have constructed some new in7nite classes of these sequences and learned some facts about their struct...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008