Extended RS code 
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 oddlike. Hence, by adding a parity check coordinate with evaluation point \(\alpha_0=0\) to an RS code on \(q1\) registers, the distance increases to \(\hat{d}=d+1\). This addition yields an \([q,k,qk+1]\) extended RS code. 

Folded RS code 
Stub. 

Maximum distance separable (MDS) code 
A \([n,k,d]_q\) \(q\)ary linear code is an MDS code if parameters \(n\), \(k\), \(d\), and \(q\) are such that the Singleton bound
\begin{align}
d \leq nk+1
\end{align}
becomes an equality. A code is called almost MDS (AMDS) when \(d=nk\). A bound for general \(q\)ary codes can also be formulated; see Thm. 1.9.10 in Ref. [1].


Maximumrank distance (MRD) code 
Also called an optimal rankdistance code. An \([n\times m,k,d]_q\) rankmetric code whose parameters are such that the Singletonlike bound
\begin{align}
k \leq \max(n, m) (\min(n, m)  d + 1)
\end{align}
become an equality.

MRD codes are matrixcode analogues of MDS codes. 
Quantum maximumdistanceseparable (MDS) code 
An \(((n,q^k,d))\) code constructed out of \(q\)dimensional qudits is an MDS code if parameters \(n\), \(k\), \(d\), and \(q\) are such that the quantum Singleton bound
\begin{align}
2(d1) \leq nk
\end{align}
becomes an equality.


ReedSolomon (RS) code 
An \([n,k,nk+1]_q\) linear code based on polynomials over \(GF(q)\). Let \(\{\alpha_1,\cdots,\alpha_n\}\) be \(n\) distinct nonzero elements of \(GF(q)\) with \(q>n\). An RS code encodes \(\mu=\{\mu_0,\cdots,\mu_{k1}\}\) into \(\{f_\mu(\alpha_1),\cdots,f_\mu(\alpha_n)\}\), with polynomial
\begin{align}
f_\mu(x)=\mu_0+\mu_1 x + \cdots + \mu_{k1}x^{k1}.
\end{align}
In other words, each codeword \(\mu\) is a string of values of the corresponding polynomial \(f_\mu\) at the points \(\alpha_i\).

Every RS code is MDS. If \(k \leq p\), then all linear MDS codes \( [n,k,nk+1]_{p^m} \) are RS codes [2]. 