Here is a list of code families which contain MDS codes.
Code Description MDS Detail
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 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.
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 n-k+1 \end{align} becomes an equality. A code is called almost MDS (AMDS) when $$d=n-k$$. A bound for general $$q$$-ary codes can also be formulated; see Thm. 1.9.10 in Ref. [1].
Maximum-rank distance (MRD) code Also called an optimal rank-distance code. An $$[n\times m,k,d]_q$$ rank-metric code whose parameters are such that the Singleton-like bound \begin{align} k \leq \max(n, m) (\min(n, m) - d + 1) \end{align} become an equality. MRD codes are matrix-code analogues of MDS codes.
Quantum maximum-distance-separable (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(d-1) \leq n-k \end{align} becomes an equality.
Reed-Solomon (RS) code An $$[n,k,n-k+1]_q$$ 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 $$\mu=\{\mu_0,\cdots,\mu_{k-1}\}$$ into $$\{f_\mu(\alpha_1),\cdots,f_\mu(\alpha_n)\}$$, with polynomial \begin{align} f_\mu(x)=\mu_0+\mu_1 x + \cdots + \mu_{k-1}x^{k-1}. \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 $$[n,k,n-k+1]_{p^m}$$ are RS codes [2].

## References

[1]
W. C. Huffman, J.-L. Kim, and P. Solé, Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021). DOI
[2]
S. Ball, “On sets of vectors of a finite vector space in which every subset of basis size is a basis”, Journal of the European Mathematical Society 733 (2012). DOI