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We use known characterizations of generalized Paley graphs which arecartesian decomposable to explicitly compute the spectra of the correspondingassociated irreducible cyclic codes. As applications, we give reductionformulas for the number of rational points in Artin-Schreier curves definedover extension fields and to the computation of Gaussian periods.

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