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Pregled bibliografske jedinice broj: 1133984

LCD codes obtained from weakly p-self-orthogonal designs


Traunkar, Ivona; Mikulić Crnković, Vedrana
LCD codes obtained from weakly p-self-orthogonal designs // G2G2 - Graphs and Groups, Geometries and GAP, Summer School
Rogla, Slovenija, 2021. str. 16-16 (predavanje, međunarodna recenzija, sažetak, znanstveni)


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Naslov
LCD codes obtained from weakly p-self-orthogonal designs

Autori
Traunkar, Ivona ; Mikulić Crnković, Vedrana

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

Skup
G2G2 - Graphs and Groups, Geometries and GAP, Summer School

Mjesto i datum
Rogla, Slovenija, 27.06.2021. - 03.07.2021

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
weakly p-self orthogonal designs, LCD codes

Sažetak
A 1-design is weakly p-self-orthogonal if all the block intersection numbers give the same residue modulo p. In [1], we analyze extensions of the incidence matrix, orbit matrix, and submatrices of the orbit matrix of a weakly p-self-orthogonal 1-design in order to construct self-orthogonal codes. A linear code is called LCD code if the intersection with its dual code is trivial. Matrix G generates an LCD code if and only if det(GG^T) is nonzero (see [3]). We extend the methods of construction described in [1] in order to construct LCD codes over finite fields. We use suitable extensions of incidence matrix, orbit matrices, and submatrices of orbit matrices in order to construct LCD codes over a finite field. We will present examples of LCD codes constructed from weakly p-self- orthogonal designs obtained from groups using the construction described in [2]. [1] V. Mikulić Crnković, I. Traunkar, Self- orthogonal codes constructed from weakly self- orthogonal designs invariant under an action of M_{; ; 11}; ; , AAECC (2021), https://doi.org/10.1007/s00200-020-00484-2. [2] D. Crnković, V. Mikulić Crnković, A. Švob, On some transitive combinatorial structures constructed from the unitary group U(3, 3), J. Statist. Plann. Inference, 144 (2014), 19-40. [3] J. L. Massey, Linear codes with complementary duals, Discrete Math. 106/107 (1992), 337–342.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekti:
HRZZ-IP-2018-01-6732 - Kombinatorički objekti i kodovi (COCo) (Crnković, Dean, HRZZ ) ( CroRIS)
NadSve-Sveučilište u Rijeci-uniri-prirod-18-111 - Permutacijske grupe kao dizajni, geometrijski dizajni i konačne geometrije (Mikulić Crnković, Vedrana, NadSve - UNIRI PROJEKTI 2018) ( CroRIS)

Ustanove:
Sveučilište u Rijeci, Fakultet za matematiku


Citiraj ovu publikaciju:

Traunkar, Ivona; Mikulić Crnković, Vedrana
LCD codes obtained from weakly p-self-orthogonal designs // G2G2 - Graphs and Groups, Geometries and GAP, Summer School
Rogla, Slovenija, 2021. str. 16-16 (predavanje, međunarodna recenzija, sažetak, znanstveni)
Traunkar, I. & Mikulić Crnković, V. (2021) LCD codes obtained from weakly p-self-orthogonal designs. U: G2G2 - Graphs and Groups, Geometries and GAP, Summer School.
@article{article, author = {Traunkar, Ivona and Mikuli\'{c} Crnkovi\'{c}, Vedrana}, year = {2021}, pages = {16-16}, keywords = {weakly p-self orthogonal designs, LCD codes}, title = {LCD codes obtained from weakly p-self-orthogonal designs}, keyword = {weakly p-self orthogonal designs, LCD codes}, publisherplace = {Rogla, Slovenija} }
@article{article, author = {Traunkar, Ivona and Mikuli\'{c} Crnkovi\'{c}, Vedrana}, year = {2021}, pages = {16-16}, keywords = {weakly p-self orthogonal designs, LCD codes}, title = {LCD codes obtained from weakly p-self-orthogonal designs}, keyword = {weakly p-self orthogonal designs, LCD codes}, publisherplace = {Rogla, Slovenija} }




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