New Binary and Ternary LCD Codes.

LCD codes are linear codes with important cryptographic applications. Recently, a method has been presented to transform any linear code into an LCD code with the same parameters when it is supported on a finite field with cardinality larger than 3. Hence, the study of LCD codes is mainly open for binary and ternary fields. Subfield subcodes of $J$ -affine variety codes are a generalization of BCH codes which have been successfully used for constructing good quantum codes. We describe binary and ternary LCD codes constructed as subfield subcodes of $J$ -affine variety codes and provide some new and good LCD codes coming from this construction. [ABSTRACT FROM AUTHOR]