Hadamard ideals and Hadamard matrices with two circulant cores
نویسندگان
چکیده
منابع مشابه
Hadamard ideals and Hadamard matrices with two circulant cores
We apply Computational Algebra methods to the construction of Hadamard matrices with two circulant cores, given by Fletcher, Gysin and Seberry. We introduce the concept of Hadamard ideal for this construction to systematize the application of Computational Algebra methods. Our approach yields an exhaustive search construction of Hadamard matrices with two circulant cores for this construction f...
متن کاملHadamard ideals and Hadamard matrices with circulant core
Computational Algebra methods have been used successfully in various problems in many fields of Mathematics. Computational Algebra encompasses a set of powerful algorithms for studying ideals in polynomial rings and solving systems of nonlinear polynomial equations efficiently. The theory of Gröbner bases is a cornerstone of Computational Algebra, since it provides us with a constructive way of...
متن کاملHeuristic algorithms for Hadamard matrices with two circulant cores
We design heuristic algorithms to construct Hadamard matrices with two circulant cores. This hard combinatorial problem can be formulated in terms of objective functions of several binary variables, so that heuristic methodologies can be used. Our algorithms are based on local and tabu search and they use information on the geometry of the objective function landscapes. In addition, we use the ...
متن کاملEncryption Schemes based on Hadamard Matrices with Circulant Cores
In this paper, we propose two encryption schemes based on Hadamard matrices with one and two circulant cores, which are classes of combinatorial designs. A cryptanalysis of the proposed schemes against some popular attacks, brute force, plaintext attacks and ciphertext attacks is explored and our study shows that these attacks does not compromise the security of the system. Furthermore, we make...
متن کاملCirculant Hadamard Matrices
Note. The determinant of a circulant matrix is an example of a group determinant, where the group is the cyclic group of order n. In 1880 Dedekind suggested generalizing the case of circulants (and more generally group de terminants for abelian groups) to arbitrary groups. It was this suggestion that led Frobenius to the creation group of representation theory. See [1] and the references therein.
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2006
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2005.03.004