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1.
Bengt R. Karlsson 《Linear algebra and its applications》2011,434(1):247-258
A three-parameter family of complex Hadamard matrices of order 6 is presented. It significantly extends the set of closed form complex Hadamard matrices of this order, and in particular contains all previously described one- and two-parameter families as subfamilies. 相似文献
2.
Dragomir Ž. Đoković 《Combinatorica》2008,28(4):487-489
Two Hadamard matrices of order 764 of Goethals-Seidel type are constructed.
The author was supported by an NSERC Discovery Grant. 相似文献
3.
A question arising in stream cypher cryptanalysis is reframed and generalized in the setting of Hadamard matrices as follows: For given n, what is the maximum value of k for which there exists a k×n(±1)-matrix A such that AAT=nIk, with each row after the first obtained by a cyclic shift of its predecessor by one position? For obvious reasons we call such matrices circulant partial Hadamard matrices. Further, what is the maximum value of k subject to the condition that the row sums are equal to r? 相似文献
4.
Majid Behbahani 《Discrete Mathematics》2006,306(23):3042-3050
We show that for each integer n for which there is a Hadamard matrix of order 4n and 8n2-1 is a prime number, there is a productive regular Hadamard matrix of order 16n2(8n2-1)2. As a corollary, by applying a recent result of Ionin, we get many parametrically new classes of symmetric designs whenever either of 4n(8n2-1)-1 or 4n(8n2-1)+1 is a prime power. 相似文献
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M. Mitrouli 《Linear algebra and its applications》2011,434(7):1761-1772
In this paper we develop a new approach for detecting if specific D-optimal designs exist embedded in Sylvester-Hadamard matrices. Specifically, we investigate the existence of the D-optimal designs of orders 5, 6, 7 and 8. The problem is motivated to explaining why specific values appear as pivot elements when Gaussian elimination with complete pivoting is applied to Hadamard matrices. Using this method and a complete search algorithm we explain, for the first time, the appearance of concrete pivot values for equivalence classes of Hadamard matrices of orders n = 12, 16 and 20. 相似文献
8.
AHowell design of side s andorder 2n, or more briefly, anH(s, 2n), is ans×s array in which each cell either is empty or contains an unordered pair of elements from some 2n-set, sayX, such that
(a) each row and each column is Latin (that is, every element ofX is in precisely one cell of each row and each column) and
(b) every unordered pair of elements fromX is in at most one cell of the array. Atrivial Howell design is anH(s, 0) havingX=? and consisting of ans×s array of empty cells. A necessary condition onn ands for the existence of a nontrivialH(s, 2n) is that 0<n≦s≦2n-1.
AnH(n+t, 2n) is said to contain a maximum trivial subdesign if somet×t subarray is theH(t, 0). This paper describes a recursive construction for Howell designs containing maximum trivial subdesigns and applies it
to settle the existence question forH(n+1, 2n)’s: forn+1 a positive integer, there is anH(n+1, 2n) if and only ifn+1 ∉ {2, 3, 5}. 相似文献
9.
The use of amicable sets of eight circulant matrices and four negacyclic matrices to generate orthogonal designs is relatively new. We find all 1841 possible orthogonal designs of order 40 in three variables, using only these new techniques. 相似文献
10.
We introduce triplet spaces for symmetric relations with defect index (1, 1) in a Pontryagin space. Representations of Pontryagin spaces by spaces of vector-valued analytic functions are investigated. These concepts are used to study 2×2-matrix valued analytic functions which satisfy a certain kernel condition. 相似文献
11.
In this paper, we introduce modular symmetric designs and use them to study the existence of Hadamard matrices modulo 5. We prove that there exist 5‐modular Hadamard matrices of order n if and only if or . In particular, this solves the 5‐modular version of the Hadamard conjecture. 相似文献
12.
C. Koukouvinos 《Discrete Mathematics》2008,308(13):2723-2731
Skew-Hadamard matrices are of special interest due to their use, among others, in constructing orthogonal designs. In this paper, we give a survey on the existence and equivalence of skew-Hadamard matrices. In addition, we present some new skew-Hadamard matrices of order 52 and improve the known lower bound on the number of the skew-Hadamard matrices of this order. 相似文献
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NianXiaohong GaoJintai 《高校应用数学学报(英文版)》1999,14(2):239-244
The robust stability for some types of tlme-varying interval raatrices and nonlineartime-varying interval matrices is considered and some sufficient conditions for robust stability of such interval matrices are given, The main results of this paper are only related to the verticesset of a interval matrices, and therefore, can be easily applied to test robust stability of interval matrices. Finally, some examples are given to illustrate the results. 相似文献
15.
Honglin Wu 《Linear algebra and its applications》2010,432(11):2909-2924
We study the 0-1 matrices whose squares are still 0-1 matrices and determine the maximal number of ones in such a matrix. The maximizing matrices are also specified. This solves a special case of a problem posed by Zhan. 相似文献
16.
Let 1 ? p ? ∞, 0 < q ? p, and A = (an,k)n,k?0 ? 0. Denote by Lp,q(A) the supremum of those L satisfying the following inequality:
17.
A note on Cartan matrices for symmetric groups 总被引:2,自引:0,他引:2
Using generating functions, a very simple explicit formula for the
determinants of the p-Cartan matrices of symmetric groups is given.
Our method works also when p is a composite number.Received: 5 September 2001 相似文献
18.
Min Fang 《Linear algebra and its applications》2011,434(3):841-848
In [2], Alon and Tarsi proposed a conjecture about the nowhere-zero point in linear mappings. In this paper, we first study some generalizations of this problem, and obtain necessary and sufficient conditions for the existence of nowhere point in these generalized problems under the assumption |F|?n+2, where n is the number of rows of the matrix A. Then we apply the results in these generalizations to give a polynomial time algebraic construction of the acyclic network codings. 相似文献
19.
Samuel Boissière 《Mathematische Zeitschrift》2006,252(3):533-555
When the quotient of a symplectic vector space by the action of a finite subgroup of symplectic automorphisms admits as a
crepant projective resolution of singularities the Hilbert scheme of regular orbits of Nakamura, then there is a natural isomorphism
between the Grothendieck group of this resolution and the representation ring of the group, given by the Bridgeland-King-Reid
map. However, this isomorphism is not compatible with the ring structures. For the Hilbert scheme of points on the affine
plane, we study the multiplicative behavior of this map. 相似文献
20.
On linear spaces and matroids of arbitrary cardinality 总被引:6,自引:0,他引:6
In this paper, we study linear spaces of arbitrary finite dimension on some
(possibly infinite) set. We interpret linear spaces as simple matroids and study the problem
of erecting some linear space of dimension n to some linear
space of dimension n + 1 if
possible. Several examples of some such erections are studied; in particular, one of these
erections is computed within some infinite iteration process.Dedicated to the memory of Gian-Carlo Rota 相似文献