Naslov
Weakly p-self-orthogonal designs and LCD codes

Autori
Ivona Traunkar, Vedrana Mikulić Crnković

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

Izvornik
Combinatorics 2022 / - , 2022, 138-138

Skup
Combinatorics 2022

Mjesto i datum
Mantova, Italija, 30.05.2022. - 03.06.2023

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
design, self-orthogonal design, LCD code

Sažetak
A 1-design is weakly p-self-orthogonal if all the block intersection num- bers gives the same residue modulo p. In [1], we analyze extensions of the incidence matrix, orbit matrix and submatrices of orbit matrix of a weakly p-self-orthogonal 1- design in order to construct self-orthogonal codes. A linear codes is called LCD code if the intersection with its dual code is trivial. Matrix G generates an LCD code if and only if det(G
GT ) 6= 0 (see [3]). We extend the methods of construction described in [1] in order to construct LCD codes over nite elds. We use suitable extensions of incidence matrix, orbit matrices and submatrices of orbit matrices in order to construct LCD codes over nite eld. We will present examples of LCD codes constructed from weakly p-self-orthogonal designs obtained from groups using construction described in [2]. [1] V. Mikulic Crnkovic, I. Traunkar, Self- orthogonal codes constructed from weakly self- orthogonal designs invariant under an action of M11, AAECC (2021), https://doi.org/10.1007/s00200- 020-00484-2. [2] D. Crnkovic, V. Mikulic Crnkovic, A. Svob, On some transitive combinatorial structures constructed from the unitary group U(3 ; 3), , J. Statist. Plann. Infer- ence, (144) 19{; ; 40, 2014., [3] J. L. Massey, Linear codes with complementary duals, Discrete Math. 106/107: 337-342, 1992.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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