Cofilling Shattering: A Syndrome-Support Hierarchy for Check Erasures

Joshua Steier

Let $A:{\mathbb{F}}_2^n\to {\mathbb{F}}_2^m$ be a binary linear map with fixed coordinate bases, let $C_A=\ker A$, and let ${\lambda }_A(y)$ be the minimum Hamming weight of a preimage of the sy…