Glasnik Matematicki, Vol. 45, No.2 (2010), 307-323.

SOME STRONGLY REGULAR GRAPHS AND SELF-ORTHOGONAL CODES FROM THE UNITARY GROUP U₄(3)

Dean Crnković, Vedrana Mikulić and B. G. Rodrigues

School of Mathematical Sciences, University of KwaZulu-Natal, Durban 4041, South Africa
e-mail: Rodrigues@ukzn.ac.za

Abstract.   We construct self-orthogonal codes from the row span over F₂ or F₃ of the adjacency matrices of some strongly regular graphs defined by the rank-3 action of the simple unitary group U₄(3) on the conjugacy classes of some of its maximal subgroups. We establish some properties of these codes and the nature of some classes of codewords.

2000 Mathematics Subject Classification.   05B05, 20D45, 94B05.

Key words and phrases.   Strongly regular graph, symmetric design, self-orthogonal design, self-orthogonal code, automorphism group.

DOI: 10.3336/gm.45.2.02

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