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Characterization and classification of optimal LCD codes
Published 9 Aug 2019 in math.CO, cs.IT, and math.IT | (1908.03294v3)
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, we determine the largest minimum weights among LCD $[n,k]$ codes over $\mathbb{F}_q$ for $(q,k) \in {(2,4), (3,2),(3,3)}$. Moreover, we give a complete classification of optimal LCD $[n,k]$ codes over $\mathbb{F}_q$ for $(q,k) \in {(2,3), (2,4), (3,2),(3,3)}$.
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