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Thep-Ranks of Skew Hadamard Designs

✍ Scribed by T.S. Michael

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
146 KB
Volume
73
Category
Article
ISSN
0097-3165

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✦ Synopsis

We use elementary linear algebra to prove that if p divides n, then the p-rank of a skew Hadamard (4n&1, 2n&1, n&1)-design is 2n. Our theorem generalizes and simplifies an extension by Jungnickel of a result of MacWilliams and Mann obtained using character theory.

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Szekeres has established the ex:stence of a skew-Hadamard malrix of order 2(9 + 1) in the case 9 = 5 (mods), a prime power. His method utilized complemlcntary difference sets in the elementary abelian group of order 9. The main result of this paper is to show that, for the same 9, there exist skew-H