nested structure of rs codes assuming a conventional disk drive wherein the error correcting capability of rs codes does not exceed 8 bytes it is necessary that 1 u2266 t and t m 1 u2266 8 assuming now u03b1 to be a primitive element in gf 256 then u03b1 is a root of the primitive polynomial p x 1 x 2 x 3 x 4 x 8 let equ1 to encode an information polynomial a x a 0 a 1 x a k 1 x k 1 in band i 1 u2266 i u2266 m the encoder proceeds as follows 1 determine equ2 as the result of dividing x 2 t m 1 a x by g x note that the encoder uses the same circuits as the encoder of a rs code with generator polynomial g x this is the code which would be used with the traditional error correcting approach each codeword is divided into two parts first the redundancy represented by the polynomial b sup i x and then the information part represented by the polynomial x 2 t i 1 a x the redundancy thus depends on the band being accessed in band i the codewords carry 2 t i 1 redundant bytes to decode assuming that band i is being accessed and the received polynomial is equ4 proceed as follows 2 apply an error erasure decoding algorithm to r sup i x assuming erasures in bytes 0 1 2 m i 1 3 produce as output the estimate a x of the information polynomial a x thus.