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Explicit Construction of Quantum Quasi-Cyclic Low-Density Parity-Check Codes with Column Weight 2 and Girth 12
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This study proposes an explicit construction method for quantum quasi-cyclic low-density parity-check (QC-LDPC) codes with a girth of 12. The proposed method designs parity-check matrices that maximize the girth while maintaining an orthogonal structure suitable for quantum error correction. By utilizing algebraic techniques, short cycles are eliminated, which improves error correction performance. Additionally, this method is extended to non-binary LDPC codes and spatially-coupled LDPC codes, demonstrating that both the girth and orthogonality can be preserved. The results of this study enable the design of high-performance quantum error-correcting codes without the need for random search.
Forward citations
Cited by 2 Pith papers
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Pair-Partition Constructions for CPM-Based Quantum LDPC Codes
A pair-partition rule for CPM exponents produces CSS-orthogonal quantum LDPC codes, and a complete, symmetry-reduced search certifies exact minimum distances for 34 finite codes.
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Sharp Error-Rate Transitions in Quantum QC-LDPC Codes under Joint BP Decoding
Joint belief propagation decoding of quantum QC-LDPC codes produces sharp error-rate transitions, with error floors dominated by few-bit error patterns.
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