On a new class of productive regular Hadamard matrices
By definition a Hadamard matrix is a \(\pm 1\)-square matrix with orthogonal rows. If the sum of rows of a Hadamard matrix \(H\) is constant then \(H\) is called regular, and it is necessarily of order \(4n^{2}\) with constant row sum \(2n\). In [\textit{Y. J. Ionin}, Des. Codes Cryptography 32, 227--233 (2004; Zbl 1047.05002)] the concept of a productive Hadamard matrix is defined and it is proved that the existence of certain productive matrices implies the existence of certain symmetric designs. In the paper under review the authors prove that if there is a Hadamard matrix of order \(4n\) and \(m=8n^{2}-1\equiv 3\pmod 4\) is a prime power, then there is a regular Hadamard matrix of order \(16n^{2}(8n^{2}-1)^{2}\). Then they proceed to show that many of the regular Hadamard matrices constructed with the above conditions are productive. Hence they apply the result of Ionin's paper quoted above to produce infinite new classes of symmetric designs.
scientific article; zbMATH DE number 5080047
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