Linear codes with arbitrary dimensional hull and pure LCD code

Maouche Youcef

Linear codes with arbitrary dimensional hull and pure LCD code

Information Theory 2023-06-02 v1 math.IT

Authors: Maouche Youcef

Abstract

In this paper, we introduce a general construction of linear codes with small dimension hull from any non LCD codes. Furthermore, we show that for any linear code $\Co$ over $\F_q$ ( $q > 3$ ) with $dim(Hull(\Co))=h$ there exist an equivalent codes $\Co_j$ with $dim(Hull(\Co_j))=j$ for any integer $0\leq j \leq h$ . We also introduce the notion of pure LCD code; an LCD code and all its equivalent are LCD; and construct an infinite family of pure LCD codes. In addition, we introduce a general construction of linear codes with one dimension hull.

Keywords

coding theory maximum distance separable code

Cite

@article{arxiv.2306.00285,
  title  = {Linear codes with arbitrary dimensional hull and pure LCD code},
  author = {Maouche Youcef},
  journal= {arXiv preprint arXiv:2306.00285},
  year   = {2023}
}

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