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Linear codes with arbitrary dimensional hull and pure LCD code (2306.00285v1)
Published 1 Jun 2023 in cs.IT and math.IT
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.