Title

Classification of generalized Hadamard matrices H(6,3) and quaternary Hermitian self-dual codes of length 18

Authors

Masaaki Harada, Tohoku University
Clement Lam, Concordia University
Akihiro Munemasa, Tohoku University
Vladimir Tonchev, Michigan Technological UniversityFollow

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://doi.org/10.37236/443

Publication Title

The Electronic Journal of Combinatorics

Recommended Citation

Harada, M., Lam, C., Munemasa, A., & Tonchev, V. (2010). Classification of generalized Hadamard matrices H(6,3) and quaternary Hermitian self-dual codes of length 18. The Electronic Journal of Combinatorics, 17, 1-14. http://doi.org/10.37236/443
Retrieved from: https://digitalcommons.mtu.edu/math-fp/103

Version

Publisher's PDF