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