Left-right Cayley complex code[1]

Cousins

• Tensor-product code— Left-right Cayley complex codewords for a fixed graph vertex are codewords of a tensor code.
• Expander code— Left-right Cayley complex codes can be viewed as Tanner-like codes on expander graphs [2], but with bits defined on squares and constraints on edges (as opposed to edges and vertices, respectively, for expander codes). Expander codes are also typically not locally testable [3].
• Balanced product (BP) code— Left-right Cayley complexes can be obtained via a balanced product of \(G\)-graphs [1].
• Quantum Tanner code— Applying the CSS construction to two left-right Cayley complex codes yields quantum Tanner codes, and one can simultaneously prove a linear distance for the quantum code and local testability for one of its constituent classical codes [4].