Article Contents
Article Contents

# Counting generalized Reed-Solomon codes

• 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 $n=6, 7, 8, 9$.

Mathematics Subject Classification: Primary: 94B27, 51E21.

 Citation:

• Table 1.  Number of GRS and MDS codes of small length and dimension 3

 $q$ $n$ $\#$ GRS $\#$ MDS $4$ $6$ $486$ $486$ $5$ $6$ $6144$ $6144$ $7$ $6$ $466560$ $1088640$ $7$ $7$ $5598720$ $5598720$ $7$ $8$ $33592320$ $33592320$ $8$ $6$ $2016840$ $6554730$ $8$ $7$ $42353640$ $141178800$ $8$ $8$ $592950960$ $2964754800$ $8$ $9$ $4150656720$ $41506567200$ $8$ $10$ $290545970400$ $290545970400$ $9$ $6$ $6881280$ $28901376$ $9$ $7$ $220200960$ $1604321280$ $9$ $8$ $5284823040$ $15854469120$ $9$ $9$ $84557168640$ $84557168640$ $9$ $10$ $676457349120$ $676457349120$
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