Quaternary codes with new parameters from two-generator simplicial complexes
For coding theorists, this provides new quaternary codes with improved parameters, though the construction method is a known technique applied to a new combinatorial structure.
The authors construct infinite families of quaternary codes from two-generator simplicial complexes, finding at least 32 new or improved codes, including a Plotkin-optimal family and 6 projective codes with best-known parameters.
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 at least 32 new or improved quaternary linear codes as per the database \cite{aydin2022updated} of best-known quaternary codes, including codes from a Plotkin-optimal family. We also report 6 projective quaternary linear codes with best-known parameters that might outperform the currently reported best-known codes due to their projectivity. Further, we establish necessary and sufficient conditions for their Gray image to be linear, which in turn gives an infinite family of Griesmer codes and several infinite families of minimal binary linear codes.