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

Access to Document

10.1007/s13226-021-00002-1

Cite this

Liao, D., & Liu, Z. (2022). Relative generalized Hamming weights over Frobenius rings. Indian Journal of Pure and Applied Mathematics, 53(2), 340-348. https://doi.org/10.1007/s13226-021-00002-1

@article{b79fd9d514a244ea9a6dfc99bc94ed9d,

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",

note = "Publisher Copyright: {\textcopyright} 2021, The Indian National Science Academy.",

year = "2022",

month = jun,

doi = "10.1007/s13226-021-00002-1",

language = "English",

volume = "53",

pages = "340--348",

journal = "Indian Journal of Pure and Applied Mathematics",

issn = "0019-5588",

publisher = "Indian National Science Academy",

number = "2",

}

TY - JOUR

T1 - Relative generalized Hamming weights over Frobenius rings

AU - Liao, Dajian

AU - Liu, Zihui

PY - 2022/6

Y1 - 2022/6

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=85107120037&partnerID=8YFLogxK

U2 - 10.1007/s13226-021-00002-1

DO - 10.1007/s13226-021-00002-1

M3 - Article

AN - SCOPUS:85107120037

SN - 0019-5588

VL - 53

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

Access to Document

Other files and links

Fingerprint

Cite this