A Eucliedan algorithm arithmetic operation system for finding an error locator polynomial σ(z) and an error evaluator polynomial ω(z) from a syndrome polynomial S(z) relative to a t-multiple error correcting Reed-Solomon code, where t is any positive integer, the system comprising:
a data storage unit (1)

for storing signals representing the syndrome polynomial S(z) and feedback signals representing an intermediate result of a Euclidean algorithm arithmetic operation and
for providing signals representing the error locator polynomical σ(z) and signals representing the error evaluator polynomial ω(z),
an arithmetic unit (2) for generating the feedback signals from the signals stored in the data storage unit (1), and
a control unit (3) for controlling the data storage unit (1) and the arithmetic unit (2).