低密度奇偶校验码
Tanner图
线性码
离散数学
扩展器代码
量子卷积码
编码(集合论)
区块代码
数学
计算机科学
组合数学
算法
解码方法
集合(抽象数据类型)
程序设计语言
作者
Anthony Leverrier,Gilles Zémor
标识
DOI:10.1109/focs54457.2022.00117
摘要
Tanner codes are long error correcting codes obtained from short codes and a graph, with bits on the edges and parity-check constraints from the short codes enforced at the vertices of the graph. Combining good short codes together with a spectral expander graph yields the celebrated expander codes of Sipser and Spielman, which are asymptotically good classical LDPC codes. In this work we apply this prescription to the left-right Cayley complex that lies at the heart of the recent construction of a c 3 locally testable code by Dinur et at. Specifically, we view this complex as two graphs that share the same set of edges. By defining a Tanner code on each of those graphs we obtain two classical codes that together define a quantum code. This construction can be seen as a simplified variant of the Panteleev and Kalachev asymptotically good quantum LDPC code, with improved estimates for its minimum distance. This quantum code is closely related to the Dinur et at. code in more than one sense: indeed, we prove a theorem that simultaneously gives a linearly growing minimum distance for the quantum code and recovers the local testability of the Dinur et at. code.
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