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Self-orthogonal codes from orbit matrices of 2- designs

In this paper we present a method for constructing self-orthogonal codes from orbit matrices of 2- designs that admit an automorphism group G which acts with orbit lengths 1 and w, where w divides |G|. This is a generalization of an earlier method proposed by Tonchev for constructing self- orthogonal codes from orbit matrices of 2-designs with a fixed-point-free automorphism of prime order. As an illustration of our method we provide a classification of self-orthogonal codes obtained from the non-fixed parts of the orbit matrices of the symmetric 2-(56, 11, 2) designs, some symmetric designs 2-(71, 15, 3) (and their residual designs), and some non-symmetric 2- designs, namely those with parameters 2-(15, 3, 1), 2-(25, 4, 1), 2-(37, 4, 1), and 2-(45, 5, 1), respectively with automorphisms of order p, where p is an odd prime. We establish that the ternary codes with parameters [10, 4, 6] and [11, 4, 6] are optimal two-weight codes. Further, we construct an optimal binary self-orthogonal [16, 5, 8] code from the non-fixed part of the orbit matrix of the 2-(64, 8, 1) design with respect to an automorphism group of order four.

2-design ; orbit matrix ; linear code ; automorphism group

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