Maximum Distance Separable Codes and Arcs in Projective Spaces

Details Maximum Distance Separable Codes and Arcs in Projective Spaces Maximum Distance Separable Codes and Arcs in Projective Spaces

2005-07-29

arxiv.org/abs/math/0507604v2

Mathematics

Combinatorics

18 Pages; co-author added; some results updated; references added

Scientific paper

Given any linear code $C$ over a finite field $GF(q)$ we show how $C$ can be described in a transparent and geometrical way by using the associated Bruen-Silverman code. Then, specializing to the case of MDS codes we use our new approach to offer improvements to the main results currently available concerning MDS extensions of linear MDS codes. We also sharply limit the possibilities for constructing long non-linear MDS codes.

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