On complementary-dual quasi-cyclic codes

A linear code C is said to be a complementary-dual code (an LCD code) if it satisfies C∩C⊥={0} where C⊥ is the dual of C. This paper is to identify few classes of LCD quasi-cyclic (QC) codes. A sufficient condition for a ρ-generator QC code C is given under which C is an LCD code. Another sufficient condition is given for maximal 1-generator codes. We provide two necessary and sufficient conditions for a maximal 1-generator QC code C satisfying certain constraints to be an LCD code. It is shown that unlike cyclic codes, a maximal 1-generator index-2 QC code is reversible if and only if it is a self-dual code. Several classes of LCD QC codes are introduced.