LCD codes over ${\mathbb{F}}_q$ are as good as linear codes for q at least four

Ruud Pellikaan

The hull $H(C)$ of a linear code $C$ is defined by $H(C)=C\cap C^{\perp }$. A linear code with a complementary dual (LCD) is a linear code with $H(C)=\{0\}$. The dimension of the hul…