Quasi-cyclic Hermitian construction of binary quantum codes
Liangdong Lu, Gaochi Zhang, Ganyu Feng, Wenzheng Ma
TL;DR
This paper introduces a new algebraic method for constructing binary quantum codes using quasi-cyclic Hermitian techniques, resulting in 30 improved codes with better minimum distances.
Contribution
It provides a sufficient condition for self-orthogonal quasi-cyclic codes and demonstrates their use in creating superior quantum codes with enhanced parameters.
Findings
30 new quantum codes with improved minimum distances
Enhanced bounds on quantum code parameters
Algebraic construction method for quantum codes
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.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Coding theory and cryptography · Quantum-Dot Cellular Automata