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Linear codes with complementary duals (abbreviated LCD) are linear codeswhose intersection with their dual are trivial. When they are binary, they playan important role in armoring implementations against side-channel attacks andfault injection attacks. Non-binary LCD codes in characteristic 2 can betransformed into binary LCD codes by expansion. In this paper, we introduce ageneral construction of LCD codes from any linear codes. Further, we show thatany linear code over $\mathbb F_{q} (q>3)$ is equivalent to an Euclidean LCDcode and any linear code over $\mathbb F_{q^2} (q>2)$ is equivalent to aHermitian LCD code. Consequently an $[n,k,d]$-linear Euclidean LCD code over$\mathbb F_q$ with $q>3$ exists if there is an $[n,k,d]$-linear code over$\mathbb F_q$ and an $[n,k,d]$-linear Hermitian LCD code over $\mathbb F_{q^2}$with $q>2$ exists if there is an $[n,k,d]$-linear code over $\mathbb F_{q^2}$.Hence, when $q>3$ (resp.$q>2$) $q$-ary Euclidean (resp. $q^2$-ary Hermitian)LCD codes possess the same asymptotical bound as $q$-ary linear codes (resp.$q^2$-ary linear codes). Finally, we present an approach of constructing LCDcodes by extending linear codes.

Linear codes over Fq which are equivalent to LCD codes