Abstract
The paper studies quasi-symmetric 2-(64, 24, 46) designs supported by minimum weight codewords in the dual code of the binary code spanned by the lines of AG(3, 22). We classify up to isomorphism all designs invariant under automorphisms of odd prime order in the full automorphism group G of the code, being of order \(\vert G\vert = 2^{13} \cdot 3^{4} \cdot 5 \cdot 7\). We show that there is exactly one isomorphism class of designs invariant under an automorphisms of order 7, 15 isomorphism classes of designs with an automorphism of order 5, and no designs with an automorphism of order 3. Any design in the code that does not admit an automorphism of odd prime order has full group of order 2m for some m ≤ 13, and there is exactly one isomorphism class of designs with full automorphism group of order 213.
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Acknowledgements
The first author gratefully acknowledges support by the National Research Foundation of South Africa through Grants # 84470 and #91495.
The second author would like to thank the University of KwaZulu-Natal for the warm hospitality during his visit. The research of this author was partially supported by an NSA grant, and a Fulbright grant #5869. The authors wish to thank the unknown referees for their useful remarks.
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Rodrigues, B.G., Tonchev, V.D. (2015). On Quasi-symmetric 2-(64, 24, 46) Designs Derived from Codes. In: Pinto, R., Rocha Malonek, P., Vettori, P. (eds) Coding Theory and Applications. CIM Series in Mathematical Sciences, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-17296-5_35
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DOI: https://doi.org/10.1007/978-3-319-17296-5_35
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17295-8
Online ISBN: 978-3-319-17296-5
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