New binary and ternary LCD codes

Carlos Galindo; Olav Geil; Fernando Hernando; Diego Ruano

doi:10.1109/tit.2018.2834500

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arXiv · 1710.00196

New binary and ternary LCD codes

Carlos Galindo·Olav Geil·Fernando Hernando·Diego Ruano

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Abstract

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.

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Carlos Galindo, Olav Geil, Fernando Hernando, Diego Ruano. 2017-09-30. New binary and ternary LCD codes. https://doi.org/10.1109/tit.2018.2834500

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