Linear codes with arbitrary dimensional hull and pure LCD code

06/01/2023

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by   Maouche Youcef, et al.

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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 over _q (q > 3) with dim(Hull())=h there exist an equivalent codes _j with dim(Hull(_j))=j for any integer 0≤ j ≤ 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.