Exact values and bounds for the optimal minimum weight of binary and ternary linear complementary dual codes are established for new infinite families, and several previously published values are corrected.
Characterization and classification of optimal LCD codes
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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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2019 1verdicts
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On the minimum weights of binary LCD codes and ternary LCD codes
Exact values and bounds for the optimal minimum weight of binary and ternary linear complementary dual codes are established for new infinite families, and several previously published values are corrected.