(81, 16, 3) Abelian difference sets do not exist
نویسندگان
چکیده
منابع مشابه
Non-Abelian Hadamard Difference Sets
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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If G is an abelian group of order u, and D is a subset of G with k elements such that every nonidentity element can be expressed 2 times in the form a b, where a and b are elements of D, then D is called a (u, k, A) difference set in G. The order n of the difference set is k 1. In this paper we consider the parameter values v = 22di 2, k = 22d+ ’ 24 ,I= 22d 2d, and n=22d. The rank r of G is the...
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This paper is motivated by R. H. Bruck’s paper[3], in which he proved that the existence of cyclic projective plane of order n ≡ 1 (mod 3) implies that of a non-planar difference set of the same order by proving that such a cyclic projective plane admits a regular non-Abelian automorphism group using n as a multiplier. In this paper we will discuss in detail the possibility of using multipliers...
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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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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1986
ISSN: 0097-3165
DOI: 10.1016/0097-3165(86)90076-2