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AMC

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 codes with parameters $[10,4,6]_3$ and $[11,4,6]_3$
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.

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