Naslov
Constructing self-orthogonal and Hermitian self-orthogonal codes via weighing matrices and orbit matrices

Autori
Crnković, Dean ; Egan, Ronan ; Švob, Andrea

Izvornik
Finite fields and their applications (1071-5797) 55 (2019); 64-77

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Weighing matrix ; orbit matrix ; Hermitian self-orthogonal code

Sažetak
We define the notion of an orbit matrix with respect to standard weighing matrices, and with respect to types of weighing matrices with entries in a finite field. In the latter case we primarily restrict our attention the fields of order 2, 3 and 4. We construct self- orthogonal and Hermitian self-orthogonal linear codes over finite fields from these types of weighing matrices and their orbit matrices respectively. We demonstrate that this approach applies to several combinatorial structures such as Hadamard matrices and balanced generalized weighing matrices. As a case study we construct self-orthogonal codes from some weighing matrices belonging to some well known infinite families, such as the Paley conference matrices, and weighing matrices constructed from ternary periodic Golay pairs.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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