A NOVEL CONSTRUCTION OF QUANTUM LDPC CODES BASED ON CYCLIC CLASSES OF LINES IN EUCLIDEAN GEOMETRIES

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The dual-containing (or self-orthogonal) formalism of Calderbank-Shor-Steane (CSS) codes provides a universal connection between a classical linear code and a Quantum Error-Correcting Code (QECC).We propose a novel class of quantum Low Density Parity Check (LDPC) codes constructed from cyclic classes of lines in Euclidean Geometry (EG).The corresponding constructed parity check matrix has quasi-cyclic structure that can be encoded flexibility,and satisfies the requirement of dual-containing quantum code.Taking the advantage of quasi-cyclic structure,we use a structured approach to construct Generalized Parity Check Matrix (GPCM).This new class of quantum codes has higher code rate,more sparse check matrix,and exactly one four-cycle in each pair of two rows.Experimental results show that the proposed quantum codes,such as EG(2,q)Ⅱ-QECC,EG(3,q)Ⅱ-QECC,have better performance than that of other methods based on EG,over the depolarizing channel and decoded with iterative decoding based on the sum-product decoding algorithm.
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