Bounding the Minimum Distance of Affine Variety Codes Using Symbolic Computations of Footprints

Date

2017-08-31

Author

GEİL, Olav
Özbudak, Ferruh

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We study a family of primary affine variety codes defined from the Klein quartic. The duals of these codes have previously been treated in [12, Example 3.2]. Among the codes that we construct almost all have parameters as good as the best known codes according to [9] and in the remaining few cases the parameters are almost as good. To establish the code parameters we apply the footprint bound [7,10] from Grobner basis theory and for this purpose we develop a new method where we inspired by Buchbergers algorithm perform a series of symbolic computations.

Subject Keywords

Affine variety codes, Buchberger's algorithm, Klein curve, Minimum distance

URI

https://hdl.handle.net/11511/49302

DOI

https://doi.org/10.1007/978-3-319-66278-7_12

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Department of Mathematics, Conference / Seminar

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Citation Formats

O. GEİL and F. Özbudak, “Bounding the Minimum Distance of Affine Variety Codes Using Symbolic Computations of Footprints,” 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/49302.