New Quaternary codes with small Plotkin-defects from two-generator simplicial complexes
Abstract
A recent characterization of all lengths of Plotkin-optimal quaternary (that is, over the ring ℤ4) codes of arbitrary type \cite{tang2025plotkin} also pins down the parameters for which no Plotkin-optimal code exists. In this article, we determine the best achievable parameters in several of these cases, obtaining codes whose minimum Lee distance is one less than the Plotkin bound, namely the codes with Plotkin-defect 1. To the best of our knowledge, this is the first attempt to study quaternary codes with Plotkin-defects. Precisely, we construct infinite families of quaternary 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 two quaternary linear code families with Plotkin-defect 1 and report at least 23 new or improved parameters having small (upto 4) Plotkin-defects, including 13 projective and 7 optimal parameters. We additionally report 4 quaternary linear codes with best-known parameters that are also projective. Further, their linear Gray images give 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.
Related
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BibTeX
@misc{yadav2026quaternary,
title = {{New Quaternary codes with small Plotkin-defects from two-generator simplicial complexes}},
author = {Ankit Yadav and Nilay Kumar Mondal and Ritumoni Sarma},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.14603},
eprint = {2605.14603},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.14603},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - New Quaternary codes with small Plotkin-defects from two-generator simplicial complexes
AU - Ankit Yadav
AU - Nilay Kumar Mondal
AU - Ritumoni Sarma
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2605.14603
UR - https://arxiv.org/abs/2605.14603
AB - A recent characterization of all lengths of Plotkin-optimal quaternary (that is, over the ring ℤ_4) codes of arbitrary type \cite{tang2025plotkin} also pins down the parameters for which no Plotkin-optimal code exists. In this article, we determine the best achievable parameters in several of these cases, obtaining codes whose minimum Lee distance is one less than the Plotkin bound, namely the codes with Plotkin-defect 1. To the best of our knowledge, this is the first attempt to study quaternary codes with Plotkin-defects. Precisely, we construct infinite families of quaternary 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 two quaternary linear code families with Plotkin-defect 1 and report at least 23 new or improved parameters having small (upto 4) Plotkin-defects, including 13 projective and 7 optimal parameters. We additionally report 4 quaternary linear codes with best-known parameters that are also projective. Further, their linear Gray images give 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.
ER -