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

Research output: Contribution to journalArticleScientificpeer-review

Standard

Orthogonality matrices for modules over finite Frobenius rings and MacWilliams' equivalence theorem. / Greferath, Marcus.

In: Finite Fields and Their Applications, Vol. 8, No. 3, 2002, p. 323-331.

Research output: Contribution to journalArticleScientificpeer-review

Harvard

APA

Vancouver

Author

Bibtex - Download

@article{78a0b7afb1cf47328dfabd6761145bd4,
title = "Orthogonality matrices for modules over finite Frobenius rings and MacWilliams' equivalence theorem",
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.",
keywords = "linear codes over rings, Frobenius rings, MacWilliams' equivalence theorem, homogeneous weights, M{\"o}bius inversion on posets",
author = "Marcus Greferath",
year = "2002",
doi = "10.1006/ffta.2001.0343",
language = "Ei tiedossa",
volume = "8",
pages = "323--331",
journal = "Finite Fields and Their Applications",
issn = "1071-5797",
publisher = "Academic Press Inc.",
number = "3",

}

RIS - Download

TY - JOUR

T1 - Orthogonality matrices for modules over finite Frobenius rings and MacWilliams' equivalence theorem

AU - Greferath, Marcus

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

KW - linear codes over rings

KW - Frobenius rings

KW - MacWilliams' equivalence theorem

KW - homogeneous weights

KW - Möbius inversion on posets

U2 - 10.1006/ffta.2001.0343

DO - 10.1006/ffta.2001.0343

M3 - Article

VL - 8

SP - 323

EP - 331

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

SN - 1071-5797

IS - 3

ER -

ID: 11261511