The punctured dodecacode is unique
Combinatorics
2026-01-14 v1
Abstract
The punctured dodecacode is an additive -ary code of length and distance which is uniformly packed. We show that a code with the same weight distribution is equivalent to it. This code is also shown to be nonlinear. We also establish the nonexistence of analogues of the dodecacode and the punctured dodecacode in Doob graphs. To that end, we classify two-weight codes of weights and in Doob and -ary Hamming graphs of diameter and the corresponding strongly regular graphs. Keywords: dodecacode, additive code, trace Hermitian duality, uniformly packed code, completely regular code, Doob graph, strongly regular graph
Keywords
Cite
@article{arxiv.2601.08008,
title = {The punctured dodecacode is unique},
author = {Markus Grassl and Denis Krotov and Lin Sok and Patrick Solé},
journal= {arXiv preprint arXiv:2601.08008},
year = {2026}
}
Comments
11+49 pages (manuscript+appendix)