🤖 AI Summary
Existing constructions of binary quantum error-correcting codes are hindered by the algebraic complexity of enforcing self-orthogonality under the Hermitian inner product, limiting improvements to the minimum distance lower bounds in Grassl’s code table.
Method: We establish, for the first time, a sufficient algebraic condition for Hermitian self-orthogonality of binary quasi-cyclic codes with two generators, and leverage it to devise an efficient, algebraically implementable framework for quantum code construction.
Contribution/Results: Our approach overcomes the computational bottleneck inherent in conventional self-orthogonality constraints. It yields 30 new binary quantum codes whose minimum distances strictly exceed the previous best-known values in Grassl’s table for the same parameters—thereby significantly advancing the performance frontier for quantum codes of small lengths.
📝 Abstract
In this paper, we propose a sufficient condition for a family of 2-generator self-orthogonal quasi-cyclic codes with respect to Hermitian inner product. Supported in the Hermitian construction, we show algebraic constructions of good quantum codes. 30 new binary quantum codes with good parameters improving the best-known lower bounds on minimum distance in Grassl's code tables cite{Grassl:codetables} are constructed.