LCD codes and LCP of codes from units of group rings

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Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol.23, no.3, pp.486-492, 2019 (Peer-Reviewed Journal) identifier


A linear code with complementary dual (LCD) is a linear code such that CC  0. LCD codes are ofgreat importance due to their wide range of applications in consumer electronics, storage systems andcryptography. Group rings have a rich source of units. Also the well-known structural linear codes such ascyclic codes are within the family of group ring codes. Thus, group rings offer an affluent source forstructural codes that may lead to linear codes with good properties. In this work, we derive a condition forcodes obtained from units of group rings to be LCD. We show that a special decomposition of group ringsmeet the LCD condition. We also proposed a consruction of linear complementary pair (LCP) of codes.