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Complete-intersection RM-type code[1]

Description

Evaluation code of polynomials evaluated on points lying on a complete intersection.

Protection

Distance bounds formulated in Ref. [2].

Member of code lists

Primary Hierarchy

Classical Domain
Galois-field Kingdom
\(q\)-ary codeECC
Additive \(q\)-ary codeECC
Linear \(q\)-ary codeECC
Evaluation codeAG ECC
Polynomial evaluation code
Parents
Polynomial evaluation code
Complete-intersection RM-type codes are polynomial evaluation codes with \(\cal X\) being a complete intersection.
Complete-intersection RM-type code

References

[1]
I. M. Duursma, C. Rentería, and H. Tapia-Recillas, “Reed-Muller Codes on Complete Intersections”, Applicable Algebra in Engineering, Communication and Computing 11, 455 (2001) DOI
[2]
L. Gold, J. Little, and H. Schenck, “Cayley–Bacharach and evaluation codes on complete intersections”, Journal of Pure and Applied Algebra 196, 91 (2005) DOI
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Zoo Code ID: complete_intersections

Cite as:
“Complete-intersection RM-type code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/complete_intersections, arXiv:2606.11484
BibTeX:
@incollection{eczoo_complete_intersections,
title={Complete-intersection RM-type code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/complete_intersections}
}
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Permanent link:
https://errorcorrectionzoo.org/c/complete_intersections

Cite as:

“Complete-intersection RM-type code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/complete_intersections, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/ag/varieties/complete_intersections.yml.