On affine variety codes from the Klein quartic

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Resumé

We study a family of primary affine variety codes defined from the Klein quartic. The duals of these codes have previously been treated in Kolluru et al., (Appl. Algebra Engrg. Comm. Comput. 10(6):433–464, 2000, Ex. 3.2). Among the codes that we construct almost all have parameters as good as the best known codes according to Grassl (2007) and in the remaining few cases the parameters are almost as good. To establish the code parameters we apply the footprint bound (Geil and Høholdt, IEEE Trans. Inform. Theory 46(2), 635–641, 2000 and Høholdt 1998) from Gröbner basis theory and for this purpose we develop a new method where we inspired by Buchberger’s algorithm perform a series of symbolic computations.
OriginalsprogEngelsk
TidsskriftCryptography and Communications
Vol/bind11
Udgave nummer2
Sider (fra-til)237-257
Antal sider21
ISSN1936-2447
DOI
StatusUdgivet - 15 mar. 2019

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title = "On affine variety codes from the Klein quartic",
abstract = "We study a family of primary affine variety codes defined from the Klein quartic. The duals of these codes have previously been treated in Kolluru et al., (Appl. Algebra Engrg. Comm. Comput. 10(6):433–464, 2000, Ex. 3.2). Among the codes that we construct almost all have parameters as good as the best known codes according to Grassl (2007) and in the remaining few cases the parameters are almost as good. To establish the code parameters we apply the footprint bound (Geil and H{\o}holdt, IEEE Trans. Inform. Theory 46(2), 635–641, 2000 and H{\o}holdt 1998) from Gr{\"o}bner basis theory and for this purpose we develop a new method where we inspired by Buchberger’s algorithm perform a series of symbolic computations.",
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On affine variety codes from the Klein quartic. / Geil, Hans Olav; Ozbudak, Ferruh.

I: Cryptography and Communications, Bind 11, Nr. 2, 15.03.2019, s. 237-257.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - On affine variety codes from the Klein quartic

AU - Geil, Hans Olav

AU - Ozbudak, Ferruh

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