English

Maximum Distance Separable Codes and Arcs in Projective Spaces

Combinatorics 2023-01-23 v2

Abstract

Given any linear code CC over a finite field GF(q)GF(q) we show how CC 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.

Keywords

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