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Decoding Affine Variety Codes Using Gröbner Bases

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Abstract

We define a class of codes that we call affine variety codes. These codes are obtained by evaluating functions in the coordinate ring of an affine variety on all the Fq-rational points of the variety. We show that one can, at least in theory, decode these codes up to half the true minimum distance by using the theory of Gröbner bases. We extend results of A. B. Cooper and of X. Chen, I. S. Reed, T. Helleseth, and T. K. Truong.

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Authors and Affiliations

  1. Department of Mathematics, James Madison University, Harrisonburg, VA, 22807

    J. Fitzgerald

  2. Department of Mathematics, LSU, Baton Rouge, LA, 70803

    R. F. Lax

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  1. J. Fitzgerald
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  2. R. F. Lax
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Fitzgerald, J., Lax, R.F. Decoding Affine Variety Codes Using Gröbner Bases. Designs, Codes and Cryptography 13, 147–158 (1998). https://doi.org/10.1023/A:1008274212057

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