In this paper, we provide a generalization of binary quadratic residue codes to the cases of higher power prime residues over the finite field of the same order, which we will call qth power residue codes. We find generating polynomials for such codes, define a new notion corresponding to the binary concept of an idempotent, and use this to find square root lower bound for the codeword weight of the duals of such codes, which leads to a lower bound on the weight of the codewords themselves. In addition, we construct a family of asymptotically bad qth power residue codes. / text

Residue codes have successfully been used for decades as a low overhead method of arithmetic error detection. This work explores the design space of residue checking for error detection in processors with modern word sizes and technology nodes. The area overheads of detecting arithmetic errors are considered for a variety of processor configurations, ranging from those best suited for embedded processors to those best for high-performance computers. The ultimate goal of this work is to enable the study of low overhead arithmetic error protection and correction in a wider variety of computer architectures than has previously been attempted in a systematic manner. / text