On bounds for codes over Frobenius rings under homogeneous weights

Marcus Greferath; Michael E. O'Sullivan

doi:10.1016/j.disc.2004.10.002

On bounds for codes over Frobenius rings under homogeneous weights

Marcus Greferath, Michael E. O'Sullivan

Not published at Aalto University

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

17 Citations (Scopus)

Abstract

Homogeneous weight functions were introduced by Heise and Constantinescu (Lineare Codes über Restklassenringen ganzer Zahlen und ihre Automorphismen bezüglich einer verallgemeinerten Hamming-Metrik, Ph.D. Thesis, Technische Universität München, 1995; Problemy Peredachi Informatsii 33(3) (1997) 22–28). They appear as a natural generalization of the Hamming weight on finite fields and the Lee weight on Z4Z4 and have proven to be important in further papers (J. Combin. Theory 92 (2000) 17–28). This article develops a Plotkin and an Elias bound for (not necessarily linear) block codes on finite Frobenius rings that are equipped with this weight.

Original language	Undefined/Unknown
Pages (from-to)	11-24
Number of pages	14
Journal	Discrete Mathematics
Volume	289
Issue number	1-3
DOIs	https://doi.org/10.1016/j.disc.2004.10.002
Publication status	Published - 2004
MoE publication type	A1 Journal article-refereed

Keywords

codes over rings
Frobenius rings
homogeneous weights
Plotkin bound
Elias boundSphere packing bound
Gilbert–Varshamov bound
ring codes

Access to Document

10.1016/j.disc.2004.10.002

http://dx.doi.org/10.1016/j.disc.2004.10.002

Cite this

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title = "On bounds for codes over Frobenius rings under homogeneous weights",

abstract = "Homogeneous weight functions were introduced by Heise and Constantinescu (Lineare Codes {\"u}ber Restklassenringen ganzer Zahlen und ihre Automorphismen bez{\"u}glich einer verallgemeinerten Hamming-Metrik, Ph.D. Thesis, Technische Universit{\"a}t M{\"u}nchen, 1995; Problemy Peredachi Informatsii 33(3) (1997) 22–28). They appear as a natural generalization of the Hamming weight on finite fields and the Lee weight on Z4Z4 and have proven to be important in further papers (J. Combin. Theory 92 (2000) 17–28). This article develops a Plotkin and an Elias bound for (not necessarily linear) block codes on finite Frobenius rings that are equipped with this weight.",

keywords = "codes over rings, Frobenius rings, homogeneous weights, Plotkin bound, Elias boundSphere packing bound, Gilbert–Varshamov bound, ring codes",

author = "Marcus Greferath and O'Sullivan, {Michael E.}",

year = "2004",

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journal = "Discrete Mathematics",

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TY - JOUR

T1 - On bounds for codes over Frobenius rings under homogeneous weights

AU - Greferath, Marcus

AU - O'Sullivan, Michael E.

PY - 2004

Y1 - 2004

N2 - Homogeneous weight functions were introduced by Heise and Constantinescu (Lineare Codes über Restklassenringen ganzer Zahlen und ihre Automorphismen bezüglich einer verallgemeinerten Hamming-Metrik, Ph.D. Thesis, Technische Universität München, 1995; Problemy Peredachi Informatsii 33(3) (1997) 22–28). They appear as a natural generalization of the Hamming weight on finite fields and the Lee weight on Z4Z4 and have proven to be important in further papers (J. Combin. Theory 92 (2000) 17–28). This article develops a Plotkin and an Elias bound for (not necessarily linear) block codes on finite Frobenius rings that are equipped with this weight.

AB - Homogeneous weight functions were introduced by Heise and Constantinescu (Lineare Codes über Restklassenringen ganzer Zahlen und ihre Automorphismen bezüglich einer verallgemeinerten Hamming-Metrik, Ph.D. Thesis, Technische Universität München, 1995; Problemy Peredachi Informatsii 33(3) (1997) 22–28). They appear as a natural generalization of the Hamming weight on finite fields and the Lee weight on Z4Z4 and have proven to be important in further papers (J. Combin. Theory 92 (2000) 17–28). This article develops a Plotkin and an Elias bound for (not necessarily linear) block codes on finite Frobenius rings that are equipped with this weight.

KW - codes over rings

KW - Frobenius rings

KW - homogeneous weights

KW - Plotkin bound

KW - Elias boundSphere packing bound

KW - Gilbert–Varshamov bound

KW - ring codes

U2 - 10.1016/j.disc.2004.10.002

DO - 10.1016/j.disc.2004.10.002

M3 - Article

VL - 289

SP - 11

EP - 24

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -