Factoring $(16, 6, 2)$ Hadamard Difference Sets
نویسندگان
چکیده
منابع مشابه
Factoring (16, 6, 2) Hadamard Difference Sets
We describe a “factoring” method which constructs all twenty-seven Hadamard (16, 6, 2) difference sets. The method involves identifying perfect ternary arrays of energy 4 (PTA(4)) in homomorphic images of a group G, studying the image of difference sets under such homomorphisms and using the preimages of the PTA(4)s to find the “factors” of difference sets in G. This “factoring” technique gener...
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Difference sets wi th pa rame te r s (v, k, 2) m a y exist even if there are no abelian (v, k, ,~) difference sets; we give the first k n o w n example of this s i tuat ion. This example gives rise to an infinite family of non -abe l i an difference sets w i th pa rameters (4t 2, 2t a t, t 2 t), where t = 2 q. 3 r5 . 1 0 ' , q, r, s >/0, and r > 0 ~ q > 0. N o abel ian difference sets w i th th...
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Using a spread of PG(3; p) and certain projective two-weight codes, we give a general construction of Hadamard diierence sets in groups H (Z p) 4 , where H is either the Klein 4-group or the cyclic group of order 4, and p is an odd prime. In the case p 3 (mod 4), we use an ovoidal bration of PG(3; p) to construct Hadamard diierence sets, this construction includes Xia's construction of Hadamard...
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This work examines the existence of (4q2,2q2 − q, q2 − q) difference sets, for q = p , where p is a prime and f is a positive integer. Suppose that G is a group of order 4q2 which has a normal subgroup K of order q such that G/K ∼= Cq × C2 × C2, where Cq,C2 are the cyclic groups of order q and 2 respectively. Under the assumption that p is greater than or equal to 5, this work shows that G does...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2008
ISSN: 1077-8926
DOI: 10.37236/836