Hemicubic code[1]

Cousins

• Quantum locally testable code (QLTC)— The hemicubic code family has asymptotically diminishing soundness that scales as order \(\Omega(1/\log n)\), locality of stabilizer generators scaling as order \(O(\log n)\), and distance of order \(\Theta(\sqrt{n})\). Soundness amplification and AEL distance amplification [2,3] can also yield improvements in various parameters [4; Table 3]. Application of generalized distance balancing [5] to hemicubic codes using an asymptotically good classical code of length \(t\) yields \(O(1/(\log(n) t^2))\) soundness and order \(\Theta(\sqrt{n}t)\) distance while maintaining locality scaling and at the expense of a dimension scaling as order \(\Theta(t^2)\) [6].
• Distance-balanced code— Application of generalized distance balancing [5] to hemicubic codes using an asymptotically good classical code of length \(t\) yields \(O(1/(\log(n) t^2))\) soundness and order \(\Theta(\sqrt{n}t)\) distance while maintaining locality scaling and at the expense of a dimension scaling as order \(\Theta(t^2)\) [6].
• Hypercube code