engleski

On some regular Hadamard matrices and associated codes

A Hadamard matrix is called regular if the row and column sums are constant. The order of a regular Hadamard matrix must be a square number. The existence of a regular Hadamard matrix of order $4m^2$ is equivalent to the existence of a symmetric $(4m^2, 2m^2−m, m^2−m)$ design, also known as a Menon design. It is conjectured that a regular Hadamard matrix of order $4m^2$ exists for every positive integer m. In this talk we give a method of constructing regular Hadamard matrices using conference graphs and Hadamard designs with skew incidence matrices (see [1]). Further, we present a construction of Siamese twin Menon designs intersecting in a BIBD and a PBD (see [2]). We also discuss codes related to these Hadamard matrices, and block designs constructed from the codes. References [1] D. Crnković. “Regular Hadamard matrices constructed from Hadamard 2-designs and conference graphs”, Discrete Math., 341:520–524, 2018. [2] D. Crnković and R. Egan. “A note on Siamese twin designs intersecting in a BIBD and a PBD”, Math. Comput. Sci., to appear.

Hadamard matrix ; linear code

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