Author

Zi-Qing Xiang

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Preprint Oct 2026

Almost all graphs are determined by their generalized spectrum

Haemers'conjecture for the generalized spectrum asserts that almost all graphs are determined by their generalized spectrum, that is, for almost all graphs $G$, every graph with the same spectrum as $G$ whose complement has the same spectrum as the complement of $G$ is isomorphic to $G$. We prove this conjecture by sho...

Zi-Qing Xiang · 0 citations

Preprint Sep 2026

Permutation automorphism groups of cyclic codes I: cyclotomic association schemes

The Berger-Charpin conjecture predicts that the permutation automorphism group of a cyclic code is generally the $q$-affine group, which is generated by the shift and the Frobenius multiplier on the index set. The word {\em generally} is not made precise in the literature, and the goal of this series of papers is to st...

Yan-Ni Wu, Zi-Qing Xiang · 0 citations