Crnkovic, Vedrana MikulicTraunkar, IvonaRodrigues, Bernardo Gabriel2024-11-122024-11-122025-08Crnkovic, V.M., Traunkar, I., Rodrigues, B.G. 2025, 'LCD codes constructed from weakly-self-orthogonal 1-designs', Advances in Mathematics of Communications, vol. 19, no. 4, pp. 1041-1056. DOI: 10.3934/amc.2024040.1930-5346 (print)1930-5338 (online)10.3934/amc.2024040http://hdl.handle.net/2263/99020By 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.en© 2024 American Institute of Mathematical Sciences.DesignWeakly p-self-orthogonal designLinear codes with complementary dual (LCD)Article