Demi-matroids from codes over finite Frobenius rings

Thomas Britz; Keisuke Shiromoto; Thomas Westerbäck

doi:10.1007/s10623-013-9895-3

Demi-matroids from codes over finite Frobenius rings

Thomas Britz^*, Keisuke Shiromoto, Thomas Westerbäck

^*Corresponding author for this work

Not published at Aalto University

Research output: Contribution to journal › Article › Scientific › peer-review

2 Citations (Scopus)

Abstract

We present a construction of demi-matroids, a generalization of matroids, from linear codes over finite Frobenius rings, as well as a Greene-type identity for rank generating functions of demi-matroids. We also prove a MacWilliams-type identity for Hamming support enumerators of linear codes over finite Frobenius rings. As a special case, these results give a combinatorial proof of the MacWilliams identity for Hamming weight enumerators of linear codes over finite Frobenius rings.

Original language	English
Pages (from-to)	97-107
Number of pages	11
Journal	DESIGNS CODES AND CRYPTOGRAPHY
Volume	75
Issue number	1
DOIs	https://doi.org/10.1007/s10623-013-9895-3
Publication status	Published - 2015
MoE publication type	A1 Journal article-refereed

Keywords

Codes over rings
Demi-matroid
MacWilliams identity

Access to Document

10.1007/s10623-013-9895-3

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abstract = "We present a construction of demi-matroids, a generalization of matroids, from linear codes over finite Frobenius rings, as well as a Greene-type identity for rank generating functions of demi-matroids. We also prove a MacWilliams-type identity for Hamming support enumerators of linear codes over finite Frobenius rings. As a special case, these results give a combinatorial proof of the MacWilliams identity for Hamming weight enumerators of linear codes over finite Frobenius rings.",

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AU - Shiromoto, Keisuke

AU - Westerbäck, Thomas

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N2 - We present a construction of demi-matroids, a generalization of matroids, from linear codes over finite Frobenius rings, as well as a Greene-type identity for rank generating functions of demi-matroids. We also prove a MacWilliams-type identity for Hamming support enumerators of linear codes over finite Frobenius rings. As a special case, these results give a combinatorial proof of the MacWilliams identity for Hamming weight enumerators of linear codes over finite Frobenius rings.

AB - We present a construction of demi-matroids, a generalization of matroids, from linear codes over finite Frobenius rings, as well as a Greene-type identity for rank generating functions of demi-matroids. We also prove a MacWilliams-type identity for Hamming support enumerators of linear codes over finite Frobenius rings. As a special case, these results give a combinatorial proof of the MacWilliams identity for Hamming weight enumerators of linear codes over finite Frobenius rings.

KW - Codes over rings

KW - Demi-matroid

KW - MacWilliams identity

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