2026/05/31 by Ankit Yadav, Nilay Kumar Mondal, Ritumoni Sarma
Computer Science · Mathematics · #cs.IT #math.IT #msc:94B05 #msc:94B25 #msc:94B60 #msc:11T71
arxiv created 2026/07/30 · arxiv updated 2026/07/31
In this article, we construct infinite families of quaternary (that is, over the ring ℤ4) CD-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.