A method for hierarchical correction coding includes converting data for a storage system into w storage device arrays, each storage device array including n storage devices, and each storage device divided into m sectors or pages. The n storage devices are grouped into l groups of t storage devices each. Erasures in the w storage device arrays are corrected based on protecting each row and column in each m×n array by an erasure-correcting code. Each group of t storage devices contains extra parities to correct extra erasures in addition to erasures corrected by vertical parities in each m×t subarray, and w, n, m, l and t are positive integers.