New Quaternary codes with small Plotkin-defects from two-generator simplicial complexes

Abstract

In this article, we construct infinite families of quaternary (that is, over the ring ${\mathbb{Z}}_4$) ${\mathcal{C}}_D$-codes, where the defining set $D$ is derived utilizing a two-generator simplicial complex, and determine their Lee weight distributions. As a result, we find three quaternary linear code families with Plotkin-defect 1 \& 2 and report at least 32 new or improved parameters having small Plotkin-defects, including 19 projective and 7 optimal parameters. We additionally report 5 quaternary linear codes with best-known parameters that are also projective. Further, we establish necessary and sufficient conditions for their Gray image to be linear, which in turn gives two infinite families of distance-optimal, one infinite family of at least almost dimension-optimal binary linear codes and five infinite families of minimal binary linear codes.