Error detection for polynomial computations

We consider the problem of error detection in a process of computation of a polynomial over the field of complex numbers or over GF(p). By errors we mean errors in the text of a program or `stuck-at? errors in a device computing a polynomial. For error detection we use linear checks constructed by the technique of Fourier transformation over the group of binary vectors. Complexity estimations, optimal checks and estimations of the error-correcting capability of these checks are obtained.