Abstract
We consider the set of ordered partitions of n into m parts acted upon by the cyclic permutation (I2 ... m). The resulting family of orbits P(n, m) is shown to have cardinality p(n, m) = (l/n) ∑d│m φ(d) (::.'!~) where φ is Euler's φ-function. P(n, m) is shown to be set-isomorphic to the family of orbits ℓ(n, m) of the set of all m-subsets of an n-set acted upon by the cyclic permutation (12 ... n). This isomorphism yields an efficient method for determining the complete weight enumerator of any code generated by a circulant matrix.
Publication Details
Razen, R, Seberry, J and Wehrhahn, K, Ordered partitions and codes generated by circulant matrices, Journal of Combinatorial Theory, Ser. A, 27(3), 1979, 333-341.