Extended RS code

Description

Stub. If \(f\in \mathcal{P}_k\) with \(k<q\), then \(\sum_{\alpha\in\mathbb{F}_q}f(\alpha)=0\) which implies RS codes are odd-like. Hence, by adding a parity check coordinate with evaluation point \(\alpha_0=0\) to an RS code on \(q-1\) registers, the distance increases to \(\hat{d}=d+1\). This addition yields an \([q,k,q-k+1]\) extended RS code.

Parent

Zoo code information

Internal code ID: extended_reed_solomon

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Zoo Code ID: extended_reed_solomon

Cite as:
“Extended RS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/extended_reed_solomon
BibTeX:
@incollection{eczoo_extended_reed_solomon, title={Extended RS code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/extended_reed_solomon} }
Permanent link:
https://errorcorrectionzoo.org/c/extended_reed_solomon

Cite as:

“Extended RS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/extended_reed_solomon

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/q-ary_digits/extended_reed_solomon.yml.