Orthogonality matrices for modules over finite Frobenius rings and MacWilliams' equivalence theorem

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Abstract

MacWilliams' equivalence theorem states that Hamming isometries between linear codes extend to monomial transformations of the ambient space. One of the most elegant proofs for this result is due to K. P. Bogart et al. (1978, Inform. and Control37, 19–22) where the invertibility of orthogonality matrices of finite vector spaces is the key step. The present paper revisits this technique in order to make it work in the context of linear codes over finite Frobenius rings.
Original languageUndefined/Unknown
Pages (from-to)323-331
Number of pages9
JournalFinite Fields and Their Applications
Volume8
Issue number3
DOIs
Publication statusPublished - 2002
MoE publication typeA1 Journal article-refereed

Keywords

  • linear codes over rings
  • Frobenius rings
  • MacWilliams' equivalence theorem
  • homogeneous weights
  • Möbius inversion on posets

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