The trace description of irreducible quasi-cyclic codes

The notion of a q-ary irreducible quasi-cyclic code of block length n and index r is introduced. A trace description of such a code is provided in a fashion similar to the trace description of irreducible cyclic codes. In particular, it is shown that an irreducible quasi-cyclic code of dimension k is completely described by an irreducible cyclic code and r elements from a field of cardinality q^k. Using this fact, a number of binary irreducible quasi-cyclic codes of index 2 are constructed and their weight spectra obtained