Finite-Ring Combinatorics and MacWilliams' Equivalence Theorem

M. Greferath, S. E. Schmidt

Tutkimustuotos: LehtiartikkeliArticleScientificvertaisarvioitu

92 Sitaatiot (Scopus)

Abstrakti

F. J. MacWilliams proved that Hamming isometries between linear codes extend to monomial transformations. This theorem has recently been genera- lized by J. Wood who proved it for Frobenius rings using character theoretic methods. The present paper provides a combinatorial approach: First we extend I. Constantinescu's concept of homogeneous weights on arbitrary finite rings and prove MacWilliams' equivalence theorem to hold with respect to these weights for all finite Frobenius rings. As a central tool we then establish a general inversion principle for real functions on finite modules that involves Möbius inversion on partially ordered sets. An application of the latter yields the aforementioned result of Wood.
AlkuperäiskieliEi tiedossa
Sivut17-28
Sivumäärä12
JulkaisuJournal of Combinatorial Theory Series A
Vuosikerta92
Numero1
DOI - pysyväislinkit
TilaJulkaistu - 2000
OKM-julkaisutyyppiA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

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