A linear code with complementary dual (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 (LCP) of codes.

A linear code with complementary dual (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 (LCP) of codes.