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Almost all graphs are determined by their generalized spectrum
Ziqing Xiang
Haemers' conjecture for the generalized spectrum asserts that almost all graphs are determined by their generalized spectrum, that is, for almost all graphs , every graph with t…
Permutation automorphism groups of cyclic codes I: cyclotomic association schemes
Yanni Wu, Ziqing Xiang
The Berger-Charpin conjecture predicts that the permutation automorphism group of a cyclic code is generally the -affine group, which is generated by the shift and the Frobenius…
Natural graph spectra
Ziqing Xiang
In 2003, van Dam and Haemers posed a fundamental question in spectral graph theory: does there exist a ``sensible'' matrix whose spectrum determines a random graph up to isomorphis…
The non-existence of some Moore polygons and spectral Moore bounds
Sebastian M. Cioabă, Vishal Gupta, Hiroshi Nozaki +1
In this paper, we study the maximum order of a connected -regular graph whose second largest eigenvalue is at most . From Alon-Boppana and Serre, we know that $v(k,θ…
Codes with symmetric distances
Gábor Hegedüs, Sho Suda, Ziqing Xiang
For a code in a space with maximal distance , we say that has symmetric distances if its distance set is symmetric with respect to . In this paper, we prov…
On Lattice Tilings of Asymmetric Limited-Magnitude Balls $\cB(n,2,m,m-1)$
Zhihao Guan, Hengjia Wei, Ziqing Xiang
Limited-magnitude errors modify a transmitted integer vector in at most entries, where each entry can increase by at most $\kp$ or decrease by at most $\km$. This channel model…
Classification of tight -designs with
Ziqing Xiang
Tight -designs are the - designs whose sizes achieve the Fisher type lower bound . Symmetric -designs, the Witt - design and t…
On the two-distance embedding in real Euclidean space of coherent configuration of type (2,2;3)
Eiichi Bannai, Etsuko Bannai, Chin-Yen Lee +2
Finding the maximum cardinality of a -distance set in Euclidean space is a classical problem in geometry. Lisoněk in 1997 constructed a maximum -distance set in …