On the existence of MRD self-dual codes

Grégory Berhuy

On the existence of MRD self-dual codes

Information Theory 2024-01-31 v2 math.IT

Authors: Grégory Berhuy

Abstract

In this paper, we investigate the existence of self-dual MRD codes $C\subset L^n$ , where $L/F$ is an arbitrary field extension of degree $m\geq n$ . We then apply our results to the case of finite fields, and prove that if $m=n$ and $F=\mathbb{F}_q$ , a self-dual MRD code exists if and only if $q\equiv n\equiv 3 \ [4].$

Keywords

MRD codes self-dual codes field extension finite fields existence conditions

Cite

@article{arxiv.2312.11341,
  title  = {On the existence of MRD self-dual codes},
  author = {Grégory Berhuy},
  journal= {arXiv preprint arXiv:2312.11341},
  year   = {2024}
}

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