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Codes from orbit matrices of strongly regular graphs

The construction of some combinatorial structures and linear codes from orbit matrices of strongly regular graphs is given in [2]. We show that under certain conditions submatrices of orbit matrices of strongly regular graphs span self-orthogonal codes (see [1]). In order to demonstrate this method of construction, we construct self-orthogonal binary linear codes from orbit matrices of the triangular graphs T(2k) with at most 120 vertices. Further, we obtain strongly regular graphs and block designs from codewords of the constructed codes. References: [1] D. Crnković, M.Maksimović and S. Rukavina, “Codes from orbit matrices of strongly regular graphs”, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan., to appear [2] D. Crnković, M. Maksimović, B. G. Rodrigues and S. Rukavina, “Self-orthogonal codes from the strongly regular graphs on up to 40 vertices”, Adv. Math. Commun., 10, 555–582, 2016.

strongly regular graph ; self-orthogonal code ; block design

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