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arXiv · 2608.05781

Symmetry-guided constructions of absolutely maximally entangled states in five open cases

Samuel Bevins·Yunus Bidav
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Abstract

We give explicit Hermitian self-dual maximum distance separable codes with parameters $[12,6,7]_{25}$, $[18,9,10]_{121}$, and $[18,9,10]_{169}$. The stabilizer construction proves the existence of ${\rm AME}(12,5)$, ${\rm AME}(18,11)$, and ${\rm AME}(18,13)$ states; one-party projection also gives ${\rm AME}(17,11)$ and ${\rm AME}(17,13)$. The first code was found by a direct search. A regular $\mathbb{Z}_3^2$ coordinate orbit of its automorphism group suggested a group-circulant form that reduces each length-eighteen construction to a nine-entry kernel. The printed matrices are certified by exact Hermitian products and complete square-minor enumeration.

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Samuel Bevins, Yunus Bidav. 2026-08-06. Symmetry-guided constructions of absolutely maximally entangled states in five open cases. https://arxiv.org/abs/2608.05781

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