Counting generalized Reed-Solomon codes
Peter Beelen, David Glynn, Tom H{\o}holdt, and Krishna Kaipa
TL;DR
This paper provides a count of generalized Reed-Solomon codes of given dimensions and lengths, including special cases involving conics, and compares these counts with existing formulas for MDS codes.
Contribution
It introduces a new counting method for GRS codes, including those from conics, and relates these counts to known MDS code formulas.
Findings
Count of GRS codes for various lengths and dimensions
Comparison with existing MDS code formulas
Extension to codes from conics
Abstract
In this article we count the number of generalized Reed-Solomon (GRS) codes of dimension k and length n, including the codes coming from a non-degenerate conic plus nucleus. We compare our results with known formulae for the number of 3-dimensional MDS codes of length n=6,7,8,9.
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Taxonomy
TopicsCoding theory and cryptography · Finite Group Theory Research · Cellular Automata and Applications