On affine variety codes from the Klein quartic View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-03

AUTHORS

Olav Geil, Ferruh Özbudak

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 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. More... »

PAGES

237-257

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s12095-018-0285-6

DOI

http://dx.doi.org/10.1007/s12095-018-0285-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1101111058


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