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Ordered partitions and codes generated by circulant matrices
Faculty of Informatics - Papers (Archive)
  • R Razen
  • Jennifer Seberry, University of Wollongong
  • K Wehrhahn
Publication Date
1-1-1979
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.

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.

Citation Information
R Razen, Jennifer Seberry and K Wehrhahn. "Ordered partitions and codes generated by circulant matrices" (1979)
Available at: http://works.bepress.com/jseberry/288/