Error location apparatus and methods

Claim 2

For an error locating decoder, means receiving a given number of data symbols and 2N check symbols, N being a positive integer, means generating 2N error syndrome signals using said received symbols and based upon a predetermined generator polynomial; means including generator polynomial means receiving said data and 2N check symbols for indicating the number of symbols in error, up to N symbols in error; the improvement being an error location apparatus, in combination: means realizing an affine polynomial for receiving said 2N syndrome signals to generate a predetermined number of root symbol signals; means selecting said root symbol signals exhibiting a predetermined Trace function; and means combining said selected root symbol signals with said syndrome signals to indicate error location.

Claim 3

Error location apparatus; means for receiving error syndrome signals relatable to N symbols in error, N is an integer of two or greater, the improvement including the combination: a syndrome buffer element for storing up to 2N syndrome signals, a work buffer store element an α i register element an α j register element a finite field element processor for receiving signals from said registers for supplying finite field result signals, a data signal buffer element, sequence means connected to all above-mentioned elements for testing operations thereof and transferring signals therebetween, said sequence means including a control store for storing program control signals defining an affine polynomial relationship between said syndrome signals whereby said above-mentioned elements interact in accordance with said affine polynomial relative to define symbols in error, and a single parity tree element in said finite element processor element element for use with any number of symbols in error.

Claim 4

Error location apparatus; means for receiving error syndrome signals relatable to N symbols in error, N is an integer of two or greater, the improvement including the combination: a syndrome buffer element for storing up to 2N syndrome signals, a work buffer store element an α i register element an α j register element a finite field element processor for receiving signals from said registers for supplying finite field result signals, a data signal buffer element, sequence means connected to all above-mentioned elements for testing operations thereof and transferring signals therebetween, said sequence means including a control store for storing program control signals defining an affine polynomial relationship between said syndrome signals whereby said above-mentioned elements interact in accordance with said affine polynomial relative to define symbols in error, and a single parity tree element in said finite element processor element element for use with any number of symbols in error.