Ordered Partitions and Codes Generated by Circulant Matrices
نویسندگان
چکیده
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 msubsets 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. Disciplines Physical Sciences and Mathematics 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. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/993 Reprinted from JOURNAL OF CoMBINATORIAL THEORY, Series A All Rights Re,erved by Academic Pre .. , New York and London VoL 27, No, 1, November 1979 Prinr.d in B.lgium Ordered Partitions and Codes Generated by Circulant Matrices
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عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 27 شماره
صفحات -
تاریخ انتشار 1979