Necessary and sufficient conditions are given for block codes to be capable of correcting up to t/sub 1/ symmetric errors, up to t/sub 2/ unidirectional errors, and up to t/sub 3/ asymmetric errors, as well as detecting from t/sub 1/+1 up to d/sub 1/ symmetric errors that are not of the unidirectional type, from t/sub 2/+1 up to d/sub 2/ unidirectional errors that are not of the asymmetric type, and from t/sub 3/+1 up to d/sub 3/ asymmetric errors. Many known conditions on block codes concerning error correction and/or detection appear as special cases of this general result. Further, some codes turn out to have stronger error correcting/detection capabilities than they were originally designed for.>

A brief introduction is given on the theory of codes correcting unidirectional errors, in the context of symmetric and asymmetric error-correcting codes. Upper bounds on the size of a code of length n correcting t or fewer unidirectional errors are then derived. Methods in which codes correcting up to t unidirectional errors are constructed by expurgating t-fold asymmetric error-correcting codes or by expurgating and puncturing t-fold symmetric error-correcting codes are also presented. Finally, tables summarizing some results on the size of optimal unidirectional error-correcting codes which follow from these bounds and constructions are given.>

A result of J.L. Massey et al. (see ibid., vol.IT-19, no.1, p.101-110, 1973) concerning weights of polynomials over GF(p/sup r/) is generalized from p=2 to general prime p. This generalization makes it possible to directly establish several theorems about polynomial weights in a way that no longer relies on results from coding theory.>

Upper bounds to the maximum number of codewords in a binary code of length n and asymmetric distance Delta are derived for some values of n and Delta . A method is given in which a code of length n-m and asymmetric distance at least t+1 is constructed by expurgating and puncturing a code of length n and Hamming distance at least 2t+1. Novel asymmetric error-correcting codes are constructed by applying this method to some celebrated symmetric error-correcting codes. a table is presented on the size of optimal asymmetric error-correcting codes of length less than 24 and asymmetric distance less than 6.>

New upper bounds on the size of codes correcting asymmetric errors are derived by sharpening some of the constraints in the integer programming problem of Delsarte and Piret. It is shown that their code for length9and asymmetric distance2is optimal.

The method of Mykkeltveit, Lam, and McEliece for finding weight enumerators of binary QR-codes is used to prove that the minimum distance of the[38,19]ternary extended QR-code is11.