Document Type

Article

Publication Date

12-10-2010

Abstract

All generalized Hadamard matrices of order 18 over a group of order 3, H(6,3),are enumerated in two different ways: once, as class regular symmetric (6,3)-nets,or symmetric transversal designs on 54 points and 54 blocks with a group of order 3 acting semi-regularly on points and blocks, and secondly,as collections of fullweight vectors in quaternary Hermitian self-dual codes of length 18. The second enumeration is based on the classification of Hermitian self-dual [18,9] codes over GF(4), completed in this paper. It is shown that up to monomial equivalence, there are 85 generalized Hadamard matrices H(6,3), and 245 inequivalent Hermitian self-dual codes of length 18 over GF(4).

Publisher's Statement

© 2010 Authors. Publisher’s version of record: https://www.combinatorics.org/ojs/index.php/eljc/article/view/v17i1r171

Publication Title

The Electronic Journal of Combinatorics

Version

Publisher's PDF

Included in

Mathematics Commons

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