Quasi-cyclic codes have provided a rich source of good linear codes. Previous constructions of quasicyclic codes have been confined mainly to codes whose length is a multiple of the dimension. In this paper it is shown how searches may be extended to codes whose length is a multiple of some integer which is greater than the dimension. The particular case of 5-dimensional codes over GF (3) is considered and a number of optimal codes (i.e., [n, k, d]-codes having largest possible minimum distance d for given length n and dimension k) are constructed. These include ternary codes with parameters [45,5, 28], [36,5, 22], [42,5, 26], [48,5, 30] and [72,5, 46], all of which improve on the previously best known bounds.

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