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The paper discusses weight distribution of periodic errors and then the optimal case on bounds of parity check digits for (n=n1+n2, k) linear codes over GF(q) that corrects all periodic errors of order r in the first block of length n1 and all periodic errors of order s in the second block of length n2 and no others. Further, we extend the study to the case when the errors are in the form of periodic errors of order r (and s) or more in the two subblocks.