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New extremal Type II ℤ4-codes of length 32 obtained from Hadamard matrices


Ban, Sara; Crnković, Dean; Mravić, Matteo; Rukavina, Sanja
New extremal Type II ℤ4-codes of length 32 obtained from Hadamard matrices // Discrete Mathematics, Algorithms and Applications, 11 (2019), 5; 1950057, 18 doi:10.1142/S1793830919500575 (međunarodna recenzija, članak, znanstveni)


Naslov
New extremal Type II ℤ4-codes of length 32 obtained from Hadamard matrices

Autori
Ban, Sara ; Crnković, Dean ; Mravić, Matteo ; Rukavina, Sanja

Izvornik
Discrete Mathematics, Algorithms and Applications (1793-8309) 11 (2019), 5; 1950057, 18

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

Ključne riječi
Hadamard matrix ; Z4 -code ; extremal Type II Z4 -code

Sažetak
For every Hadamard design with parameters 2-(n −1, n/2-1, n/4-1) having a skew-symmetric incidence matrix we give a construction of 54 Hadamard designs with parameters 2-(4n − 1, 2n − 1, n − 1). Moreover, for the case n = 8 we construct doubly-even self-orthogonal binary linear codes from the corresponding Hadamard matrices of order 32. From these binary codes we construct five new extremal Type II Z 4 -codes of length 32. The constructed codes are the first examples of extremal Type II Z 4 -codes of length 32 and type 4^k1 2^k2 , k1 ∈ {; ; 7, 8, 9, 10}; ; , whose residue codes have minimum weight 8. Further, correcting the results from the literature we construct 5147 extremal Type II Z4 -codes of length 32 and type 4^14 2^4.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekt / tema
HRZZ-IP-2018-01-6732 - Kombinatorički objekti i kodovi (Dean Crnković, )

Ustanove
Sveučilište u Rijeci - Odjel za matematiku

Profili:

Avatar Url Sanja Rukavina (autor)

Avatar Url Dean Crnković (autor)

Avatar Url Sara Ban (autor)

Avatar Url Matteo Mravić (autor)

Citiraj ovu publikaciju

Ban, Sara; Crnković, Dean; Mravić, Matteo; Rukavina, Sanja
New extremal Type II ℤ4-codes of length 32 obtained from Hadamard matrices // Discrete Mathematics, Algorithms and Applications, 11 (2019), 5; 1950057, 18 doi:10.1142/S1793830919500575 (međunarodna recenzija, članak, znanstveni)
Ban, S., Crnković, D., Mravić, M. & Rukavina, S. (2019) New extremal Type II ℤ4-codes of length 32 obtained from Hadamard matrices. Discrete Mathematics, Algorithms and Applications, 11 (5), 1950057, 18 doi:10.1142/S1793830919500575.
@article{article, year = {2019}, pages = {18}, DOI = {10.1142/S1793830919500575}, chapter = {1950057}, keywords = {Hadamard matrix, Z4 -code, extremal Type II Z4 -code}, journal = {Discrete Mathematics, Algorithms and Applications}, doi = {10.1142/S1793830919500575}, volume = {11}, number = {5}, issn = {1793-8309}, title = {New extremal Type II ℤ4-codes of length 32 obtained from Hadamard matrices}, keyword = {Hadamard matrix, Z4 -code, extremal Type II Z4 -code}, chapternumber = {1950057} }

Časopis indeksira:


  • Web of Science Core Collection (WoSCC)
    • Emerging Sources Citation Index (ESCI)
  • Scopus


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