Maximum Distance Separable Codes and Arcs in Projective Spaces
Combinatorics
2023-01-23 v2
Abstract
Given any linear code over a finite field we show how 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.
Cite
@article{arxiv.math/0507604,
title = {Maximum Distance Separable Codes and Arcs in Projective Spaces},
author = {T. L. Alderson and A. A. Bruen and R. Silverman},
journal= {arXiv preprint arXiv:math/0507604},
year = {2023}
}
Comments
18 Pages; co-author added; some results updated; references added