Further Results on the Relative Generalized Hamming Weight

Zihui Liu; Yao Wei

doi:10.1109/TIT.2021.3078064

Further Results on the Relative Generalized Hamming Weight

Zihui Liu^*, Yao Wei

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

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

2 Citations (Scopus)

Abstract

Based on the applications to the wire-tap channel and bounds on the relative generalized Hamming weight, we will introduce optimal codes of type mathcal {I} and type mathcal {II}. We will give some necessary conditions and the explicit construction for a linear code mathcal {C} to be optimal of type mathcal {I} and mathcal {II} with respect to a subcode mathcal {C}_{1}. We will also present a new bound on two different parameters of the relative generalized Hamming weight.

Original language	English
Pages (from-to)	6344-6355
Number of pages	12
Journal	IEEE Transactions on Information Theory
Volume	67
Issue number	10
DOIs	https://doi.org/10.1109/TIT.2021.3078064
Publication status	Published - Oct 2021

Keywords

Relative generalized Hamming weight
relative subcode
relative subspace
value assignment
wire-tap channel

Access to Document

10.1109/TIT.2021.3078064

Cite this

@article{8888b4ab32284e03bcb66e3f61002fab,

title = "Further Results on the Relative Generalized Hamming Weight",

abstract = "Based on the applications to the wire-tap channel and bounds on the relative generalized Hamming weight, we will introduce optimal codes of type mathcal {I} and type mathcal {II}. We will give some necessary conditions and the explicit construction for a linear code mathcal {C} to be optimal of type mathcal {I} and mathcal {II} with respect to a subcode mathcal {C}_{1}. We will also present a new bound on two different parameters of the relative generalized Hamming weight.",

keywords = "Relative generalized Hamming weight, relative subcode, relative subspace, value assignment, wire-tap channel",

author = "Zihui Liu and Yao Wei",

note = "Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2021",

month = oct,

doi = "10.1109/TIT.2021.3078064",

language = "English",

volume = "67",

pages = "6344--6355",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "10",

}

TY - JOUR

T1 - Further Results on the Relative Generalized Hamming Weight

AU - Liu, Zihui

AU - Wei, Yao

PY - 2021/10

Y1 - 2021/10

N2 - Based on the applications to the wire-tap channel and bounds on the relative generalized Hamming weight, we will introduce optimal codes of type mathcal {I} and type mathcal {II}. We will give some necessary conditions and the explicit construction for a linear code mathcal {C} to be optimal of type mathcal {I} and mathcal {II} with respect to a subcode mathcal {C}_{1}. We will also present a new bound on two different parameters of the relative generalized Hamming weight.

AB - Based on the applications to the wire-tap channel and bounds on the relative generalized Hamming weight, we will introduce optimal codes of type mathcal {I} and type mathcal {II}. We will give some necessary conditions and the explicit construction for a linear code mathcal {C} to be optimal of type mathcal {I} and mathcal {II} with respect to a subcode mathcal {C}_{1}. We will also present a new bound on two different parameters of the relative generalized Hamming weight.

KW - Relative generalized Hamming weight

KW - relative subcode

KW - relative subspace

KW - value assignment

KW - wire-tap channel

UR - http://www.scopus.com/inward/record.url?scp=85105853689&partnerID=8YFLogxK

U2 - 10.1109/TIT.2021.3078064

DO - 10.1109/TIT.2021.3078064

M3 - Article

AN - SCOPUS:85105853689

SN - 0018-9448

VL - 67

SP - 6344

EP - 6355

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 10

ER -

Further Results on the Relative Generalized Hamming Weight

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this