Naslov
On some regular Hadamard matrices and associated codes

Autori
Crnković, Dean

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Combinatorics 2018 / - , 2018, 55-55

Skup
Combinatorics 2018 conference

Mjesto i datum
Arco, Italija, 03.06.2018. - 09.06.2018

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Hadamard matrix ; linear code

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA