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}
}
  • Tai Do Duc, Bernhard Schmidt
  • Published in J. Comb. Theory, Ser. A 2019
  • Mathematics, Computer Science
  • 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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    SHOWING 1-10 OF 15 REFERENCES

    B

    • K. H. Leung
    • Schmidt: Nonexistence Results on Generalized Bent Functions Zq → Zq with Oddm and q ≡ 2 ( mod 4). J. Combin. Theory Ser. A 163
    • 2019
    VIEW 2 EXCERPTS

    J

    • G. Hiranandani
    • M. Schlenker: Small Circulant Complex Hadamard Matrices of Butson Type. Eur. J. Com. 51
    • 2016
    VIEW 1 EXCERPT

    B

    • K. H. Leung, S. L. Ma
    • Schmidt: Nonexistence of Abelian Difference Sets: Lander’s Conjecture for Prime Power Orders. Trans. Amer. Math. Soc. 356
    • 2004

    Design Theory (2nd edition)

    • T. Beth, D. Jungnickel, H. Lenz
    • 1999