Patent ID: 7039853

Claim:
A Reed-Solomon decoding method based upon a simplified PGZ algorithm, wherein a syndrome polynomial S(x) of received data is computer for obtaining an error location polynomial σ(x) and an error value polynomial ω(x) to perform error corrections in the received data for at least one error(s) with a number no more than t; said Reed-Solomon decoding method comprising the steps of: defining a syndrome matrix S t×t and a syndrome vector s t×1 from the syndrome polynomial S(x) to solve S t×t σ t×1 =S t×1 ; and solving a determinant A t of the syndrome matrix S t×t to define a new error location polynomial Φ(x)=A t σ(x) and Ω(x)=A t ω(x), which are then used to obtain error location(s) and error value(s) purely utilizing finite field adders and finite field multipliers without finite field inverters, wherein the defining step further includes a step of determining the number of errors t by checking whether the rows in the syndrom matrix S t×t are linearly dependent.