Abstract
If H is a regular Hadamard matrix with row sum 2h, m is a positive integer, and q = (2h − 1)2, then (4h 2(q m + 1 − 1)/(q −1),(2h 2 − h)q m,(h 2-h)q m) are feasible parameters of a symmetric designs. If q is a prime power, then a balanced generalized weighing matrix BGW((q m +1 − 1)/(q−1),q m,q m−q m −1) can be applied to construct such a design if H satisfies certain structural conditions. We describe such conditions and show that if H satisfies these conditions and B is a regular Hadamard matrix of Bush type, then B×H satisfies these structural conditions. This allows us to construct parametrically new infinite families of symmetric designs.
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Ionin, Y.J. Regular Hadamard Matrices Generating Infinite Families of Symmetric Designs. Designs, Codes and Cryptography 32, 227–233 (2004). https://doi.org/10.1023/B:DESI.0000029225.69728.39
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DOI: https://doi.org/10.1023/B:DESI.0000029225.69728.39