Patent ID: 7134067

Claim:
A method for decoding a d-bit syndrome of FIRE code, a syndrome obtained from the checking of a message or data packet encoded according to a degree-d generator polynomial characteristic of said codes, said degree-d generator including a factor from which a Galois Field (GF) can be built, said method comprising the steps of: splitting said syndrome into sub-syndromes including at least a left sub-syndrome (LSS) and a right sub-syndrome (RSS) on the basis of the structure of said generator polynomial; combining said sub-syndromes to form at least one kind of error pattern; picking from said at least one kind of error pattern an error pattern (EP), said picking step comprising the steps of: picking an error pattern having the least spread between bits in error among said at least one kind of error pattern; and selecting accordingly a mode of correction; determining from said picked error pattern if an uncorrectable error is detected; decoding from said at least left sub-syndrome and right sub-syndrome to determine if errors are confined within a first d-bit of said message or data packet; and correcting errors within said message or data packet comprising the steps of: picking said left sub-syndrome or said right sub-syndrome depending on what mode of correction has been selected; determining a rank of said picked sub-syndrome in said Galois field; determining a rank of said picked error pattern in said Galois field; subtracting, modulo the length of said Galois field, from the rank of said picked sub-syndrome the rank of said picked error pattern, thereby obtaining a group first vector (GFV); and decoding whether said GFV matches with a group corresponding to said mode of correction.