LCD codes and LCP of codes from units of group rings

Authors : Mehmet Emin KÖROĞLU

Pages : 486-492

Doi:10.16984/saufenbilder.459123

View : 14 | Download : 7

Publication Date : 2019-06-01

Article Type : Research Paper

Abstract :A linear code with complementary dual insert ignore into journalissuearticles values(LCD); is a linear code such that  LCD codes are of great importance due to their wide range of applications in consumer electronics, storage systems and cryptography. Group rings have a rich source of units. Also the well-known structural linear codes such as cyclic codes are within the family of group ring codes. Thus, group rings offer an affluent source for structural codes that may lead to linear codes with good properties. In this work, we derive a condition for codes obtained from units of group rings to be LCD. We show that a special decomposition of group rings meet the LCD condition. We also proposed a consruction of linear complementary pair insert ignore into journalissuearticles values(LCP); of codes.
Keywords : group rings, unit derived codes, LCD codes