Patent ID: 8347169

Claim:
A non-transitory computer readable medium including a method for creating codewords using common partial parity products, the method comprising: an algorithm module accepting 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; the algorithm module setting a value for a first minimum number of first common mathematical operations and a value for a second minimum umber of second mathematical operations, where the first common mathematical operations are different than the second common mathematical operations; the algorithm module finding a first group of parity bit positions, where the parity bit for each position in the first group is calculated using at least the first minimum number of first common mathematical operations; the algorithm module finding a second group of parity bit positions, where the parity bit for each position in the second group is calculated using at least the second minimum number of second common mathematical operations; and, a codeword generation module subtracting the first and second common mathematical operations from the first and second group of parity bit position calculations, and finding unique mathematical operations associated with each parity bit position calculation in the first and second group.