Abstract:
By a suitable extension of incidence matrices, orbit matrices, and
submatrices of orbit matrices of weakly p-self-orthogonal 1-designs, in this paper
we describe a construction of LCD codes over a finite field. To illustrate
the construction, we determine some binary LCD codes from self-orthogonal
1-designs which are invariant under the transitive non-regular action of the alternating
group of order 60. With the described construction, we have obtained
6 optimal codes and 3 near-optimal codes.
