The Plotkin-Type Bound on the Generalized Symbol-Pair Weight and Symbol-Pair Equiweight Codes

Yinghao Liang; Zihui Liu

doi:10.1109/TIT.2024.3392744

The Plotkin-Type Bound on the Generalized Symbol-Pair Weight and Symbol-Pair Equiweight Codes

Yinghao Liang, Zihui Liu^*

^*Corresponding author for this work

Beijing Institute of Technology

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

1 Citation (Scopus)

Abstract

We present the Plotkin-type bound on the generalized symbol-pair weight and show that all the symbol-pair equiweight codes achieve the Plotkin-type bound. Some new judging criteria are given for symbol-pair equiweight codes, and based on these judging criteria, we show the existence of a class of symbol-pair equiweight codes by design and graph theory. Also, we explicitly construct the symbol-pair version simplex code by the action of a group on a set. Furthermore, we construct several classes of inequiweight codes achieving the Plotkin-type bound.

Original language	English
Article number	10507095
Pages (from-to)	4990-5001
Number of pages	12
Journal	IEEE Transactions on Information Theory
Volume	70
Issue number	7
DOIs	https://doi.org/10.1109/TIT.2024.3392744
Publication status	Published - 1 Jul 2024
Externally published	Yes

Keywords

Hamilton cycle
Plotkin-type bound
Symbol-pair weight
block intersection graph
generalized value assignment

Access to Document

10.1109/TIT.2024.3392744

Cite this

@article{e440088f45b74b33adecae6fc526bcda,

title = "The Plotkin-Type Bound on the Generalized Symbol-Pair Weight and Symbol-Pair Equiweight Codes",

abstract = "We present the Plotkin-type bound on the generalized symbol-pair weight and show that all the symbol-pair equiweight codes achieve the Plotkin-type bound. Some new judging criteria are given for symbol-pair equiweight codes, and based on these judging criteria, we show the existence of a class of symbol-pair equiweight codes by design and graph theory. Also, we explicitly construct the symbol-pair version simplex code by the action of a group on a set. Furthermore, we construct several classes of inequiweight codes achieving the Plotkin-type bound.",

keywords = "Hamilton cycle, Plotkin-type bound, Symbol-pair weight, block intersection graph, generalized value assignment",

author = "Yinghao Liang and Zihui Liu",

note = "Publisher Copyright: {\textcopyright} 2024 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.",

year = "2024",

month = jul,

day = "1",

doi = "10.1109/TIT.2024.3392744",

language = "English",

volume = "70",

pages = "4990--5001",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

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

number = "7",

}

TY - JOUR

T1 - The Plotkin-Type Bound on the Generalized Symbol-Pair Weight and Symbol-Pair Equiweight Codes

AU - Liang, Yinghao

AU - Liu, Zihui

PY - 2024/7/1

Y1 - 2024/7/1

N2 - We present the Plotkin-type bound on the generalized symbol-pair weight and show that all the symbol-pair equiweight codes achieve the Plotkin-type bound. Some new judging criteria are given for symbol-pair equiweight codes, and based on these judging criteria, we show the existence of a class of symbol-pair equiweight codes by design and graph theory. Also, we explicitly construct the symbol-pair version simplex code by the action of a group on a set. Furthermore, we construct several classes of inequiweight codes achieving the Plotkin-type bound.

AB - We present the Plotkin-type bound on the generalized symbol-pair weight and show that all the symbol-pair equiweight codes achieve the Plotkin-type bound. Some new judging criteria are given for symbol-pair equiweight codes, and based on these judging criteria, we show the existence of a class of symbol-pair equiweight codes by design and graph theory. Also, we explicitly construct the symbol-pair version simplex code by the action of a group on a set. Furthermore, we construct several classes of inequiweight codes achieving the Plotkin-type bound.

KW - Hamilton cycle

KW - Plotkin-type bound

KW - Symbol-pair weight

KW - block intersection graph

KW - generalized value assignment

UR - https://www.scopus.com/pages/publications/85191307096

U2 - 10.1109/TIT.2024.3392744

DO - 10.1109/TIT.2024.3392744

M3 - Article

AN - SCOPUS:85191307096

SN - 0018-9448

VL - 70

SP - 4990

EP - 5001

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 7

M1 - 10507095

ER -

The Plotkin-Type Bound on the Generalized Symbol-Pair Weight and Symbol-Pair Equiweight Codes

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this