The weight distribution of families of reducible cyclic codes through the weight distribution of some irreducible cyclic codes

The calculation of the weight distribution for some reducible cyclic codes can be reduced down to the corresponding one of a particular kind of irreducible cyclic codes. This reduction is achieved by means of a known identity (see [3,Theorem 1.1]). In fact, as will be shown here, the weight distribution of some families of reducible cyclic codes, recently reported in several works ([2,5,7,11,12]), and that of others not previously reported, can be obtained almost directly by means of this identity.