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Ordered partitions and codes generated by circulant matrices

Journal Article


Abstract


  • We consider the set of ordered partitions of n into m parts acted upon by the cyclic permutation (12...m). The resulting family of orbits P(n, m) is shown to have cardinality p(n,m)=( 1 n∑ d mφ(d)( n d m d), where φ is Euler's φ-function. P(n, m) is shown to be set-isomorphic to the family of orbits C(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. © 1979.

Publication Date


  • 1979

Citation


  • Razen, R., Seberry, J., & Wehrhahn, K. (1979). Ordered partitions and codes generated by circulant matrices. Journal of Combinatorial Theory, Series A, 27(3), 333-341. doi:10.1016/0097-3165(79)90021-9

Scopus Eid


  • 2-s2.0-49249152203

Web Of Science Accession Number


Start Page


  • 333

End Page


  • 341

Volume


  • 27

Issue


  • 3

Abstract


  • We consider the set of ordered partitions of n into m parts acted upon by the cyclic permutation (12...m). The resulting family of orbits P(n, m) is shown to have cardinality p(n,m)=( 1 n∑ d mφ(d)( n d m d), where φ is Euler's φ-function. P(n, m) is shown to be set-isomorphic to the family of orbits C(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. © 1979.

Publication Date


  • 1979

Citation


  • Razen, R., Seberry, J., & Wehrhahn, K. (1979). Ordered partitions and codes generated by circulant matrices. Journal of Combinatorial Theory, Series A, 27(3), 333-341. doi:10.1016/0097-3165(79)90021-9

Scopus Eid


  • 2-s2.0-49249152203

Web Of Science Accession Number


Start Page


  • 333

End Page


  • 341

Volume


  • 27

Issue


  • 3