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In coding theory, a very interesting problem (but at the same time, a verydifficult one) is to determine the weight distribution of a given code. Thisproblem is even more interesting for cyclic codes, and this is so, mainlybecause they possess a rich algebraic structure, which can be utilized in avariety of ways. For example, in Engineering Telecommunications, this structureis commonly employed to design very efficient coding and decoding algorithms.In this note, we are going to use a characterization of all semiprimitivetwo-weight irreducible cyclic codes over any finite field, recently presentedin [8], in order to determine the full weight distribution of any irreduciblecyclic code over any finite field of dimension two. In fact, the relevance ofour results is that by means of them we can actually directly determine thefull weight distribution of any irreducible cyclic code, of dimension one ortwo, just by knowing its length.

Determining the full weight distribution of any irreducible cyclic code over any finite field of dimension two