Abstract
A code of lengthn, dimensionk and minimum distanced ismaximum distance separable (MDS) ifk+d=n+1. We give the number of MDS codes of length 7 and dimension 3 on finite fields withq elements whereq=2m. In order to get this number, we compute the number of configurations of seven points in the projective plane overF q , no three of which are collinear.
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Rolland, R. The number of MDS [7, 3] codes on finite fields of characteristic 2. AAECC 3, 301–310 (1992). https://doi.org/10.1007/BF01294838
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DOI: https://doi.org/10.1007/BF01294838