Maximum Distance Separable Codes and Arcs in Projective Spaces

T. L. Alderson; A. A. Bruen; R. Silverman

doi:10.1016/j.jcta.2006.11.005

Maximum Distance Separable Codes and Arcs in Projective Spaces

组合数学 2023-01-23 v2

作者: T. L. Alderson , A. A. Bruen , R. Silverman

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摘要

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.

关键词

coding theory distance sets combinatorial designs

引用

@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}
}

备注

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

Maximum Distance Separable Codes and Arcs in Projective Spaces

摘要

关键词

引用

备注

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