Characterization and classification of optimal LCD codes

Abstract

Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. We give a characterization of LCD codes over $$\mathbb {F}_q$$ having large minimum weights for $$q \in \{2,3\}$$ . Using the characterization, for arbitrary n, we determine the largest minimum weights among LCD [n, k] codes over $$\mathbb {F}_q$$ , where $$(q,k) \in \{(2,4), (3,2),(3,3)\}$$ . Moreover, for arbitrary n, we give a complete classification of optimal LCD [n, k] codes over $$\mathbb {F}_q$$ , where $$(q,k) \in \{(2,3), (2,4), (3,2),(3,3)\}$$ .