On the Weight Distribution of the Dual of some Cyclic Codes with Two Non Conjugated Zeros

An important family of codes for error control in digital communications are the so-called cyclic codes; therefore,finding the weight distribution of a q-ary cyclic code C is not only a problem of theoretical interest, but also of practicalimportance. Typically, when the finite field q is a prime field, the problem is handled by expressing the Hammingweight of each codeword in C by means of certain combination of exponential sums. In this work, we will present anew method for computing the weight distribution of the dual of some cyclic codes with two non conjugated zeros. Aswe will see, such distribution is also given by means of the evaluation of certain exponential sums, however, suchevaluation is only needed to be done over a subset. Moreover, this method has the advantage of flexibility, in thesense that it can also be applied to cyclic codes over finite fields of non prime order.