A system and method are provided for creating codewords using common partial parity products. The method initially accepts an algorithm for creating p indexed parity bit positions, where the parity bit for each position is calculated from mathematical operations performed on bits from n indexed user word positions. A first group of parity bit positions is found, where the parity bit for each position in the first group is calculated using at least a first number of common mathematical operations. A second group of parity bit positions is found, where the parity bit for each position in the second group is calculated using at least a second number of common mathematical operations. The common mathematical operations are subtracted from the first and second group of parity bit position calculations, so that unique mathematical operations can be found, associated with each parity bit position calculation in the first and second group.