Homological Error Correcting Codes and Systolic Geometry

Abstract

In my masters thesis I prove a square root bound on the distance of homological codes that come from two dimensional surfaces, as a result of the systolic inequality. I also give a detailed version of M.H. Freedman's proof that due to systolic freedom, this bound does not hold in higher dimensions.

Cited by in corpus (4)

• Constructions and Noise Threshold of Hyperbolic Surface Codes
• Quantum error-correcting codes and 4-dimensional arithmetic hyperbolic manifolds
• ${\mathbb{Z}}_2$-coefficient homology $(1,2)$-systolic freedom of $\mathbb{R}{\mathbb{P}}^3$ # $\mathbb{R}{\mathbb{P}}^3$
• Hypermap-Homology Quantum Codes (Ph.D. thesis)