Abstract
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.
Keywords
Group code
Linear code
Group (periodic table)
Code (set theory)
Block code
Cryptography
Dual (grammatical number)
Mathematics
Computer science
Discrete mathematics
Algorithm
Physics
Decoding methods
Subject Areas
Coding theory and cryptography
·Artificial Intelligence ·Physical Sciences
Cooperative Communication and Network Coding
·Computer Networks and Communications ·Physical Sciences
graph theory and CDMA systems
·Electrical and Electronic Engineering ·Physical Sciences
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