Naslov
LCD codes from weighing matrices

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

Izvornik
Applicable algebra in engineering communication and computing (0938-1279) 32 (2021); 175-189

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

Ključne riječi
Weighing matrix ; Orbit matrix ; LCD code

Sažetak
Linear codes with complementary duals are linear codes whose intersection with their duals are trivial, shortly named LCD codes. In this paper we outline a construction for LCD codes over finite fields of order q using weighing matrices and their orbit matrices. The LCD codes constructed can be of any length and dimension according to the choice of matrices used in their construction. As a special case, LCD codes of length 2n and dimension n are constructed which also have the property of being formally self-dual. Alternatively, under a condition depending on q that the codes are not LCD, this method constructs self-dual codes. To illustrate the method we construct LCD codes from weighing matrices, including the Paley conference matrices and Hadamard matrices. We also extend the construction to Hermitian LCD codes over the finite field of order 4. In addition, we propose a decoding algorithm that can be feasible for the LCD codes obtained from some of the given methods.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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