New binary and ternary LCD codes

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.

References in corpus (2)

• Linear codes over Fq which are equivalent to LCD codes
• Erasure Techniques in MRD codes

Cited by in corpus (8)

• Entanglement-assisted quantum error-correcting codes over arbitrary finite fields
• A recursive construction for projective Reed-Muller codes
• Entanglement-assisted quantum error-correcting codes from subfield subcodes of projective Reed-Solomon codes
• Locally recoverable $J$-affine variety codes
• Subfield subcodes of projective Reed-Muller codes
• Galois hulls of MDS codes and their quantum error correction
• New Constructions of MDS Twisted Reed-Solomon Codes and LCD MDS Codes
• Binary LCD Codes from ${\mathbb{Z}}_2{\mathbb{Z}}_2[u]$