To reduce the time required for arithmetic operation of a syndrome relating to the case of decoding a code word which is able to correct a t- multiple error for a series consisting of 255 sets consecutive symbols each in 8-bit structure being an element on an extended Galois field.

A prescribed number from a symbol series of a code word, for example, two partial series consisting of symbols extracted by two each are generated, and a partial arithmetic means 10 is provided to each partial series and a partial syndrome with respect to each partial series is calculated simultaneously in parallel, an overall arithmetic means 20 combines two partial syndromes to integrate the result into a syndrome Sp relating to the code word, then repetitive arithmetic operations of 255 times having been required by a conventional system is reduced to 128 times. Then the syndrome arithmetic time is reduced to a half.