We study subsets of Grassmann varieties over a field , such that these subsets are unions of Schubert cycles, with respect to a fixed flag. We study such sets in detail, and give applications to coding theory, in particular for Grassmann codes. For much is known about such Schubert unions with a maximal number of -rational points for a given spanning dimension. We study the case and give a conjecture for general . We also define Schubert union codes in general, and study the parameters and support weights of these codes.
Seminaires Et Congres, 2009, p. 103-123
Main Research Area:
Arithmetics, Geometry, and coding Theory - AGCT, 2009