A General Description for the Weight Distribution of Some Reducible Cyclic Codes

A remarkably general result which provides the evaluation of a family of exponential sums was presented by Moisio [10] in 2000. In this work, we use such a general result in order to determine the value distribution of a particular kind of exponential sum. Then, motivated by some new ideas of Ma, et al. [9], we use this value distribution in order to formulate a general description for the weight distribution of a particular kind of reducible cyclic codes that has been recently studied. As will be shown, such a general description not only gives a unified explanation for these families of codes, but also gives the weight distribution for other reducible cyclic codes that have not been studied so far. In addition, among the kind of codes studied here, we will characterize those that are projective.