This invention relates to an error correction upon reproduction of digital signals. The error correction is performed by decoding code words such as cross-interleaved Reed Solomon codes, in which first code blocks are formed by a plurality of information words which are in the first arrangement state and a plurality of first check words which are produced by codes associated with the plurality of information words with a Hamming distance of d,, and second code blocks are formed by a plurality of information words and a plurality of first check words which are in the second arrangement state and which consist of the said plurality of information words and the said plurality of first check words which are respectively included in the different first code blocks, and by a plurality of second check words which are produced by codes associated with the plurality of information words and the plurality of first check words with a Hamming distance of d 2 . At the first decoding stage, at least errors are detected and at the same time the flags indicative of the decoding states are i added with respect to the second code blocks. At the second decoding stage, in accordance with the contents of the flags and on the basis of a combination of p 2 and q selected from their combinations satisfying 2p 2 +q≤d 1 -1, errors are detected and errors of p 2 words are corrected and erasures of q words to which the flags were added are corrected with respect to the first code blocks.