Characterization and classification of optimal LCD codes
2021
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 $$(q,k) \in \{(2,3), (2,4), (3,2),(3,3)\}$$
.
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