This is code written for the OSCAR computer algebra system which aims to construct finite fields in a standardized way. The fields are constructed in a way that avoids the usage of Conway polynomials.
The ideas used are described by Lübeck in [1] and some of the code is based on Lübeck's StandardFF GAP package.
This code runs in Julia using the OSCAR computer algebra package, which requires Julia 1.6 or newer. It can be installed as follows.
julia> using Pkg
julia> Pkg.add("Oscar")
julia> using OscarFor more detailed information, please consult the installation instructions on the OSCAR website.
[1] Lübeck, F. Standard generators of finite fields and their cyclic subgroups, Journal of Symbolic Computation (2023)(https://arxiv.org/pdf/2107.02257.pdf).