Counting generalized Reed-Solomon codes
Peter Beelen, David G. Glynn, Tom Høholdt, Krishna V. Kaipa · Advances in Mathematics of Communications · 2017
In this article we count the number of $[n, k]$ generalized Reed-Solomon (GRS) codes, including the codes coming from a non-degenerate conic plus nucleus. We compare our results with known formulae for the number of $[n, 3]$ MDS codes with $n=6, 7, 8, 9$.