English

The punctured dodecacode is unique

Combinatorics 2026-01-14 v1

Abstract

The punctured dodecacode is an additive 44-ary code of length 1111 and distance 55 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 66 and 88 in Doob and 44-ary Hamming graphs of diameter 99 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)

R2 v1 2026-07-01T09:01:40.102Z