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On Hadamard matrices of order 2(p+1) with an automorphism of odd prime order p

✍ Scribed by Daniel B. Dalan; Masaaki Harada; Akihiro Munemasa


Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
126 KB
Volume
11
Category
Article
ISSN
1063-8539

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✦ Synopsis


Abstract

In this paper, we investigate Hadamard matrices of order 2(p + 1) with an automorphism of odd prime order p. In particular, the classification of such Hadamard matrices for the cases p = 19 and 23 is given. Self‐dual codes related to such Hadamard matrices are also investigated. Β© 2003 Wiley Periodicals, Inc. J Combin Designs 11: 367–380, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10052


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Let p be an odd prime number such that p -1 = 2 e m for some odd m and e β‰₯ 2. In this article, by using the special linear fractional group PSL(2, p), for each i, 1 ≀ i ≀ e, except particular cases, we construct a 2-design with parameters v = p + 1, k = (p -1)/2 i + 1 and Ξ» = ((p-1)/2 i +1)(p-1)/2 =