Relative generalized Hamming weights over Frobenius rings

Dajian Liao; Zihui Liu

doi:10.1007/s13226-021-00002-1

Relative generalized Hamming weights over Frobenius rings

Dajian Liao, Zihui Liu^*

^*Corresponding author for this work

School of Mathematics and Statistics

Jiangsu Ocean University

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

Abstract

We show that a commutative ring which can be applied to the wire-tap channel of type II with the coset coding scheme is a Frobenius one. Relative generalized Hamming weights (RGHWs) are then generalized to codes over Frobenius rings. The basic properties and descriptions of RGHWs for codes over Frobenius rings are presented.

Original language	English
Pages (from-to)	340-348
Number of pages	9
Journal	Indian Journal of Pure and Applied Mathematics
Volume	53
Issue number	2
DOIs	https://doi.org/10.1007/s13226-021-00002-1
Publication status	Published - Jun 2022

Keywords

Frobenius rings
relative generalized Hamming weights
the coset coding scheme
wire-tap channel

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10.1007/s13226-021-00002-1

Cite this

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title = "Relative generalized Hamming weights over Frobenius rings",

abstract = "We show that a commutative ring which can be applied to the wire-tap channel of type II with the coset coding scheme is a Frobenius one. Relative generalized Hamming weights (RGHWs) are then generalized to codes over Frobenius rings. The basic properties and descriptions of RGHWs for codes over Frobenius rings are presented.",

keywords = "Frobenius rings, relative generalized Hamming weights, the coset coding scheme, wire-tap channel",

author = "Dajian Liao and Zihui Liu",

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AU - Liao, Dajian

AU - Liu, Zihui

PY - 2022/6

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AB - We show that a commutative ring which can be applied to the wire-tap channel of type II with the coset coding scheme is a Frobenius one. Relative generalized Hamming weights (RGHWs) are then generalized to codes over Frobenius rings. The basic properties and descriptions of RGHWs for codes over Frobenius rings are presented.

KW - Frobenius rings

KW - relative generalized Hamming weights

KW - the coset coding scheme

KW - wire-tap channel

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DO - 10.1007/s13226-021-00002-1

M3 - Article

AN - SCOPUS:85107120037

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SP - 340

EP - 348

JO - Indian Journal of Pure and Applied Mathematics

JF - Indian Journal of Pure and Applied Mathematics

IS - 2

ER -

Relative generalized Hamming weights over Frobenius rings

Abstract

Keywords

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