New binary and ternary LCD codes
Carlos Galindo, Olav Geil, Fernando Hernando, Diego Ruano
TL;DR
This paper introduces new binary and ternary LCD codes constructed as subfield-subcodes of $J$-affine variety codes, expanding the options for cryptographic applications and quantum code construction.
Contribution
It presents a novel construction method for binary and ternary LCD codes using subfield-subcodes of $J$-affine variety codes, filling a gap in the study of LCD codes over small fields.
Findings
New binary LCD codes with improved parameters
New ternary LCD codes with enhanced properties
Demonstrated effectiveness of subfield-subcode construction
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 -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 -affine variety codes and provide some new and good LCD codes coming from this construction.
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