LCD codes constructed from weakly-self-orthogonal 1-designs

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.