MRD-codes and linear sets

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Abstract

In this paper we point out the relationship between linear MRD-codes and various geometric objects as linearized polynomials, linear sets of PG(n1,qn), and generalized Segre varieties. We introduce and characterize a class of particular linear MRD-codes called Fqn-linear codes with distance nk+1 proving that such codes are equivalent to (nk+1)-embeddings of a canonical subgeometry.

Keywords

MRD-code
Linearized polynomial
Linear set
Fq-linear representation
Segre variety

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Partially supported by MIUR and by GNSAGA of INdAM.