Paper Info
Title
Classification of generalized Hadamard matrices H(6,3) and quaternary Hermitian self-dual codes of length 18
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 full weight 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 in equivalent Hermitian self-dual codes of length 18 over GF(4).
Year
Venue
Field
2010
ELECTRONIC JOURNAL OF COMBINATORICS
Discrete mathematics,Hadamard's maximal determinant problem,Combinatorics,Hadamard matrix,Matrix (mathematics),Transversal (geometry),Monomial,Complex Hadamard matrix,Hermitian matrix,Hadamard transform,Mathematics
DocType
Volume
Issue
Journal
17.0
1.0
ISSN
Citations 
PageRank 
1077-8926
6
0.62
References 
Authors
10
4
Name
Order
Citations
PageRank
Masaaki Harada136769.47
Clement Lam2599.25
Akihiro Munemasa311426.25
Vladimir D. Tonchev440776.90