engleski

Self-orthogonal doubly-even codes from Hadamard matrices of order 48

From 54 Hadamard (47, 23, 12) designs we construct 15 doubly-even binary linear codes with parameters [48, 24, 4], [48, 23, 4], [48, 14, 4], [48, 14, 8], [48, 14, 12], [48, 13, 12], [48, 13, 16] and [48, 13, 8]. The constructed codes are self-complementary and self-orthogonal, and the [48, 24, 4] codes are self-dual. Further, we describe a construction of strongly regular graphs with parameters (495, 238, 109, 119), (276, 44, 22, 4), (78, 22, 11, 4), (77, 16, 0, 4), and (66, 20, 10, 4) from support designs of the constructed codes.

Hadamard matrix; doubly-even code; self-orthogonal code; strongly regular graph

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