2023/06/01 by Youcef, Maouche
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2306.00285
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 \Fq (q > 3) with dim(Hull(\Co))=h there exist an equivalent codes \Coj with dim(Hull(\Coj))=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.