Infinite families of LCD codes and their weight distributions

Abstract

We construct infinite families of binary or ternary linear complementary dual (LCD) codes, which arise from some families of self-orthogonal codes associated with simplicial complexes or multi-variable functions. We find explicit criteria for self-orthogonal codes to preserve self-orthogonality after augmentation. For the construction of LCD codes, we either directly use some families of self-orthogonal codes or we use the augmented codes of these self-orthogonal code families. As a result, we obtain several infinite families of binary or ternary LCD codes, which include LCD-optimal families and at least LCD-almost optimal families; we also present their weight distributions. We mention that our LCD code families are new compared with the data summarized in [27, Table 5] based on the previously known LCD code families.