Skew-hadamard abelian group difference sets
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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In 1933 a family of skew Hadamard difference sets was described by Paley using matrix language and was called the Paley–Hadamard difference sets in the literature. During the last 70 years, no new skew Hadamard difference sets were found. It was conjectured that there are no further examples of skew Hadamard difference sets. This conjecture was proved to be true for the cyclic case in 1954, and...
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Skew Hadamard difference sets have been an interesting topic of study for over 70 years. For a long time, it had been conjectured the classical Paley difference sets (the set of nonzero quadratic residues in Fq where q ≡ 3 mod 4) were the only example in Abelian groups. In 2006, the first author and Yuan disproved this conjecture by showing that the image set of D5(x2, u) is a new skew Hadamard...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1966
ISSN: 0021-8693
DOI: 10.1016/0021-8693(66)90029-9