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 [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 Gröbner basis theory and for this purpose we develop a new method where we inspired by Buchbergers algorithm perform a series of symbolic computations.
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Acknowledgments
The authors gratefully acknowledge the support from The Danish Council for Independent Research (Grant No. DFF–4002-00367). They are also grateful to Department of Mathematical Sciences, Aalborg University for supporting a one-month visiting professor position for the second listed author. The research of Ferruh Özbudak has been funded by METU Coordinatorship of Scientific Research Projects via grant for projects BAP-01-01-2016-008 and BAP-07-05-2017-007.
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Geil, O., Özbudak, F. (2017). Bounding the Minimum Distance of Affine Variety Codes Using Symbolic Computations of Footprints. In: Barbero, Á., Skachek, V., Ytrehus, Ø. (eds) Coding Theory and Applications. ICMCTA 2017. Lecture Notes in Computer Science(), vol 10495. Springer, Cham. https://doi.org/10.1007/978-3-319-66278-7_12
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DOI: https://doi.org/10.1007/978-3-319-66278-7_12
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