Journal article
Generalized Hamming weights of affine Cartesian codes
Let F be any field and A1,…,Am be finite subsets of F. We determine the maximum number of common zeroes a linearly independent family of r polynomials of degree at most d of F[x1,…,xm] can have in A1×…×Am. In the case when F is a finite field, our results resolve the problem of determining the generalized Hamming weights of affine Cartesian codes.
This is a generalization of the work of Heijnen and Pellikaan where these were determined for the generalized Reed–Muller codes. Finally, we determine the duals of affine Cartesian codes and compute their generalized Hamming weights as well.
Language: | English |
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Year: | 2018 |
Pages: | 130-145 |
ISSN: | 10715797 and 10902465 |
Types: | Journal article |
DOI: | 10.1016/j.ffa.2018.01.006 |
ORCIDs: | Beelen, Peter and Datta, Mrinmoy |
Affine Cartesian codes Affine Hilbert functions Algebra Cartesians Codes (symbols) Data Processing Finite element method Finite fields Finite subsets Generalized Hamming weight Generalized Hamming weights Hilbert functions Linearly independents Numerical Methods Zero dimensional varieties Zero-dimensional