The weight distribution of irreducible cyclic codes associated with decomposable generalized Paley graphs

We use known characterizations of generalized Paley graphs which are cartesian decomposable to explicitly compute the spectra of the corresponding associated irreducible cyclic codes. As applications, we give reduction formulas for the number of rational points in Artin-Schreier curves defined over extension fields and to the computation of Gaussian periods.
20 pages, 2 tables. Added information on Cartesian products of graphs. A general reviwe was made, with small additions improving readability. Some typos corrected. arXiv admin note: text overlap with arXiv:1908.08097