The punctured dodecacode is unique | Sciact

The punctured dodecacode is unique Full article

Journal

Mathematics and Education in Mathematics
ISSN: 1313-3330 , E-ISSN: 2815-4002

Output data

Year: 2026, Pages: 393-404 Pages count : 12 DOI: 10.55630/mem.2026.55.393-404

Tags

dodecacode, additive code, trace Hermitian duality, uniformly packed code, completely regular code, Doob graph, strongly regular graph

Authors

Grassl M. ¹ , Krotov D. ² , Sok L. ³ , Solé P. ⁴

Affiliations

1	International Centre for Theory of Quantum Technologies, University of Gdansk, Gdansk, Poland
2	Sobolev Institute of Mathematics Novosibirsk 630090, Russia
3	School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
4	I2M (Aix Marseille Univ, CNRS), Marseilles, France

Funding (1)

Министерство науки и высшего образования РФ

FWNF-2026-0011

The punctured dodecacode is an additive 4-ary code of length 11 and distance 5 which is uniformly packed. We show that any code with the same weight distribution is equivalent to it. This code is also shown to be nonlinear. We also establish the nonexistence of analogs of the dodecacode and the punctured dodecacode in Doob graphs. To that end, we classify two-weight codes of weights 6 and 8 in Doob graphs and 4-ary Hamming graphs of diameter 9 and the corresponding strongly regular graphs.

Grassl M. , Krotov D. , Sok L. , Solé P.
The punctured dodecacode is unique
Mathematics and Education in Mathematics. 2026. P.393-404. DOI: 10.55630/mem.2026.55.393-404 OpenAlex

Submitted:	Jan 12, 2026
Published online:	May 19, 2026

≡ OpenAlex:

W7161587216