On affine variety codes from the Klein quartic
| Autor: | Ferruh Özbudak, Olav Geil |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Code (set theory)
Series (mathematics) Computer Networks and Communications Applied Mathematics Computation Klein quartic 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology 01 natural sciences Klein curve Algebra Gröbner basis Computational Theory and Mathematics 010201 computation theory & mathematics Affine variety codes 0202 electrical engineering electronic engineering information engineering Dual polyhedron Quartic surface Affine variety Mathematics |
| Zdroj: | Geil, H O & Ozbudak, F 2019, ' On affine variety codes from the Klein quartic ', Cryptography and Communications, vol. 11, no. 2, pp. 237-257 . https://doi.org/10.1007/s12095-018-0285-6 |
| ISSN: | 1936-2455 1936-2447 |
| DOI: | 10.1007/s12095-018-0285-6 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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