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Hyperplane Sections of Grassmannians and the Number of MDS Linear Codes

โœ Scribed by Sudhir R. Ghorpade; Gilles Lachaud

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
474 KB
Volume
7
Category
Article
ISSN
1071-5797

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โœฆ Synopsis

We obtain some e!ective lower and upper bounds for the number of (n, k)-MDS linear codes over % O . As a consequence, one obtains an asymptotic formula for this number. These results also apply for the number of inequivalent representations over % O of the uniform matroid or, alternatively, the number of % O -rational points of certain open strata of Grassmannians. The techniques used in the determination of bounds for the number of MDS codes are applied to deduce several geometric properties of certain sections of Grassmannians by coordinate hyperplanes.

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