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The Encyclopedia of Integer Sequences
"... This article gives a brief introduction to the OnLine Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs ..."
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Cited by 634 (15 self)
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This article gives a brief introduction to the OnLine Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs to generate the sequence, references, links to relevant web pages, and other
Hadamard Matrices, Orthogonal Designs and Construction Algorithms
"... We discuss algorithms for the construction of Hadamard matrices. We include discussion of construction using Williamson matrices, Legendre pairs and the discret Fourier transform and the two circulants construction. Next we move to algorithms to determine the equivalence of Hadamard matrices using t ..."
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Cited by 4 (1 self)
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We discuss algorithms for the construction of Hadamard matrices. We include discussion of construction using Williamson matrices, Legendre pairs and the discret Fourier transform and the two circulants construction. Next we move to algorithms to determine the equivalence of Hadamard matrices using the pro le and projections of Hadamard matrices. A summary is then given which considers inequivalence of Hadamard matrices of orders up to 44. The nal two sections give algorithms for constructing orthogonal designs, short amicable and amicable sets for use in the Kharaghani array. 1 Algorithms for constructing Hadamard matrices 1.1 Hadamard matrices constructed from Williamson matrices An Hadamard matrix H of order n has elements 1 and satis es HH T = nI n . These matrices are used extensively in coding and communications (see Seberry and Yamada [90]). The order of an Hadamard matrix is 1, 2 or n (0 mod 4). The rst unsolved case is order 428. We use Williamson's construction as the basis of our algorithm to construct a distributed computer search for new Hadamard matrices. We briey describe the theory of Williamson's construction below. Previous computer searches for Hadamard matrices using Williamson's condition 2 are described in Section 1.1.1. The implementation of the search algorithm is presented in Section 1.1.2, and the results of the search are described in Section 1.1.3. Theorem 1 (Williamson [104]) Suppose there exist four (1; 1) matrices A, B, C, D of order n which satisfy XY T = Y X T ; X;Y 2 fA; B; C; Dg Further, suppose AA T +BB T + CC T +DD T = 4nI n (1) Then H = 2 6 6 6 4 A B C D B A D C C D A B D C B A 3 7 7 7 5 (2) is an Hadamard matrix of order 4n constructed from a Williamson array. Let the matrix T given below be called ...
Extremal doubly even (56,28,12) codes and Hadamard matrices of order 28, Australas
 J. Combin
, 1994
"... Abstract. In [2] Bussemaker and Tonchev constructed six doubly even (56,28, 12) codes from two Hadamard matrices of order 28. But two of them were not distinguished. In [11] and [12] we characterized Hadamard matrices of order 28 and there are exactly 487 Hadamard matrices, up to equivalence. In thi ..."
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Abstract. In [2] Bussemaker and Tonchev constructed six doubly even (56,28, 12) codes from two Hadamard matrices of order 28. But two of them were not distinguished. In [11] and [12] we characterized Hadamard matrices of order 28 and there are exactly 487 Hadamard matrices, up to equivalence. In this paper we show that only two of the above 487 matrices produce six doubly even (56,28,12) codes and that two of the six codes are equivalent. Therefore there are exactly five (56,28,12) codes, up to equivalence, produced by Hadamard matrices of order 28. 1.