31. Data decoding apparatus according to claim 30, wherein said parity check matrix is a Reed-Solomon parity check matrix H, selected from the group consisting of ##EQU13## where .alpha. is a root of a polynomial F(X) which is irreducible over a galois field GF(2).
30. Data decoding apparatus for decoding a digital information signal and correcting errors occurring therein during transmission by application of a series of first check words and a series of second check words, the transmitted digital signal being received as a block of digital data words of a predetermined bit length m, and which includes said series of first check words and said series of second check words, each such series having k check words, comprising input means for receiving said transmitted digital signal as a first block formed of the words of the information signal and said series of first and second check words; first decoder means coupled to said input means for decoding the received digital data words and the first and second check words and correcting the digital data words and the series of first check words by said series of second check words; deinterleaving means for delaying each of the words of the digital data signal and of the first series of check words by a respective different amount and arranging such words in a different arranging order, thereby providing a second block formed of the words of the information signal and the first check words; second decoder means coupled to said deinterleaving means for decoding the words of the digital data signal and the first series of check words so arranged and for correcting the digital data words by said first series of check words to provide a third block of said data words; and output means coupled to said second decoder means to receive said third block for providing the corrected digital signal; wherein each of said first and second decoder means decodes by generating syndromes according to a parity check matrix having n columns and k rows, and in which each element of one predetermined row is selected from digital values from zero to 2.sup.m -1, so that the same value does not appear twice in said predetermined row, and in which the elements in the remaining rows are selected to be of a given power, for all the elements in each respective row, where m is the bit length of said data words and n is the number of words in each block formed of the digital data words and the associated check words.