Here is a list of $$q$$-ary linear codes over the Galois field $$GF(q)$$.
Code Description
Alternant code Stub.
Bose–Chaudhuri–Hocquenghem (BCH) code Stub.
Divisible code A linear $$q$$-ary code is $$\Delta$$-divisible if the Hamming weight of each of its codewords is divisible by $$\Delta$$. A $$2$$-divisible ($$4$$-divisible) code is called even (doubly even) [1]. A code is called singly even if all codewords are even and at least one has weight equal to 2 modulo 4.
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.
Gabidulin code Also called a vector rank-metric code. A linear code over $$GF(q^N)$$ that corrects errors over rank metric instead of the traditional Hamming distance. Every element $$GF(q^N)$$ can be written as an $$N$$-dimensional vector with coefficients in $$GF(q)$$, and the rank of a set of elements is rank of the matrix formed by their coefficients.
Generalized Reed-Solomon (GRS) code Stub.
Goppa code Let $$G(z)$$ be a polynomial describing a projective plane curve with coefficients from $$GF(q^m)$$ for some fixed integer $$m$$. Let $$L$$ be a finite subset of the extension field $$GF(q^m)$$ where $$q$$ is prime, meaning $$L = \{\alpha_1, \cdots, \alpha_n\}$$ is a subset of nonzero elements of $$GF(q^m)$$. A Goppa code $$\Gamma(L,G)$$ is an $$[n,k,d]$$ linear code consisting of all vectors $$a = a_1, \cdots, a_n$$ such that $$R_a(z) =0$$ modulo $$G(z)$$, where $$R_a(z) = \sum_{i=1}^n \frac{a_i}{z - \alpha_i}$$.
Linear $$q$$-ary code An $$(n,K,d)_q$$ linear code is denoted as $$[n,k,d]_q$$, where $$k=\log_{q}K$$ need not be an integer. Its codewords form a linear subspace, i.e., for any codewords $$x,y$$, $$\alpha x+ \beta y$$ is also a codeword for any $$q$$-ary digits $$\alpha,\beta$$.
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. [2].
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 $$\alpha_i$$.
Two-weight code Stub.
Wozencraft ensemble code Stub.
$$q$$-ary group code An $$[n,k]_{q}$$ code based on a finite group $$G$$ of size $$n$$. A group code for an abelian group is called an abelian group code.

## References

[1]
Sascha Kurz, “Divisible Codes”. 2112.11763
[2]
W. C. Huffman, J.-L. Kim, and P. Solé, Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021). DOI