1. In an advanced RAID system, having at least one array of n disks wherein n is a positive integer greater than or equal to 2, and a set of m redundancy disks associated with said at least one array wherein m is a positive integer greater than or equal to 3, said system further includes data and redundancy data in the form of a set of word segments residing in the above disks, said word segments having equal length and predetermined size, a method for updating redundancy information, comprising: providing a first expression of redundancy data in terms of a first summation of a sequence of data, said sequence including a summation of data segments; providing a second expression of redundancy data in terms of a second summation, wherein the elements of said second summation includes elements of the first summation having each of the elements contained therein multiplied by a first sequence of co-effiecients; providing a m th expression of redundancy data in terms of a (m−1) th summation of a sequence of data, wherein the elements of said (m−1) th summation includes elements of the m th summation having each of the elements multiplied by a (m−1) th sequence of co-effiecients; computing said first expression having at most m unknown values; computing said second expression having at most m unknown values, and second expression includes a set of translation of said sequence of data, said translation of data being subjected to conditions including for any 2 given words w and w′ T k (w&plus;w′)&equals;T k (w)&plus;Tk(w′); and computing a (m−1) th set of values representing said m th sequence of coefficients; thereby a large set of coefficients for first to m− 1 expressions can be carefully selected for use in redundancy calculations for at most m disk failures.