# Bilinear forms on finite abelian groups and group-invariant Butson Hadamard matrices

@article{Duc2019BilinearFO, title={Bilinear forms on finite abelian groups and group-invariant Butson Hadamard matrices}, author={Tai Do Duc and Bernhard Schmidt}, journal={J. Comb. Theory, Ser. A}, year={2019}, volume={166}, pages={337-351} }

Abstract Let K be a finite abelian group and let exp ( K ) denote the least common multiple of the orders of the elements of K. A BH ( K , h ) matrix is a K-invariant | K | × | K | matrix H whose entries are complex hth roots of unity such that H H ⁎ = | K | I , where H ⁎ denotes the complex conjugate transpose of H, and I is the identity matrix of order | K | . Let ν p ( x ) denote the p-adic valuation of the integer x. Using bilinear forms on K, we show that a BH ( K , h ) exists whenever… CONTINUE READING

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