Quasi-Cyclic Constructions of Quantum Codes
Carlos Galindo, Fernando Hernando, Ryutaroh Matsumoto
TL;DR
This paper develops algebraic methods to construct good quantum codes from quasi-cyclic codes, providing conditions for self-orthogonality, bounds on code weights, and explicit parameters for the resulting quantum codes.
Contribution
It introduces new algebraic constructions of quantum codes based on quasi-cyclic codes with specific orthogonality properties, advancing quantum error correction techniques.
Findings
Established sufficient conditions for self-orthogonality of quasi-cyclic codes.
Derived lower bounds for symplectic weight and minimum distance.
Constructed explicit quantum codes with improved parameters.
Abstract
We give sufficient conditions for self-orthogonality with respect to symplectic, Euclidean and Hermitian inner products of a wide family of quasi-cyclic codes of index two. We provide lower bounds for the symplectic weight and the minimum distance of the involved codes. Supported in the previous results, we show algebraic constructions of good quantum codes and determine their parameters.
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