Abstract
We prove a Weil-Serre type bound on the number of solutions of a class of reducible additive equations over finite fields. Using the trace representation of cyclic codes, this enables us to write a general estimate for the weights of cyclic codes. We extend Wolfmann's weight bound to a larger classes of cyclic codes. In particular, our result is applicable to any cyclic code over Fp and Fp 2 , where p is an arbitrary prime. Examples indicate that our bound performs very well against the Bose-Chaudhuri-Hocquenghem (BCH) bound and that it yields the exact minimum distance in some cases
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