The punctured dodecacode is unique
DOI:
https://doi.org/10.55630/mem.2026.55.393-404Keywords:
dodecacode, additive code, trace Hermitian duality, uniformly packed code, completely regular code, Doob graph, strongly regular graphAbstract
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.
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