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.
Similar content being viewed by others
References
Hirschfeld J. W. P.: Projective geometries over finite fields. Oxford: Clarendon Press, 1979
Macwilliams F. J., Sloane N. J. A.: The theory of error-correcting codes. Amsterdam: North-Holland, 1977
Oberst U., Dur A.: A constructive characterization of all optimal linear codes, Seminaire d'Algbre Paul Dubreil et Marie Paule Malliavin, Proceedings, Paris, 1983–1984. Lecture Notes in Math. Vol. 1146. Berlin, Heidelberg, New York: Springer 1985
Skorobogatov A. N.: Strata of Grassmannians, and a problem of Segre, Proceeding of AGCT-3, Luminy, June 17, 1991, Lecture Notes in Math. Berlin, Heidelberg, New York: Springer (to appear)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01294838