New Bounds and Constructions for Multiply Constant-Weight Codes

Xin Wang; Hengjia Wei; Chong Shangguan; Gennian Ge

doi:10.1109/TIT.2016.2609389

New Bounds and Constructions for Multiply Constant-Weight Codes

Xin Wang, Hengjia Wei, Chong Shangguan, Gennian Ge

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

10 Scopus citations

Abstract

Multiply constant-weight codes (MCWCs) were introduced recently to improve the reliability of certain physically unclonable function response. In this paper, the bounds of MCWCs and the constructions of optimal MCWCs are studied. First, we derive three different types of upper bounds which improve the Johnson-type bounds given by Chee et al. for some parameters. The asymptotic lower bound of MCWCs is also examined. Then, we obtain the asymptotic existence of two classes of optimal MCWCs, which shows that the Johnson-type bounds for MCWCs with distances 2 Σ_i=1^m w_i - 2 or 2mw - 2w are asymptotically exact. Finally, we construct a class of optimal MCWCs with total weight four and distance six by establishing the connection between such MCWCs and a new kind of combinatorial structures. As a consequence, the maximum sizes of MCWCs with total weight less than or equal to four are determined almost completely.

Original language	English
Article number	7567498
Pages (from-to)	6315-6327
Number of pages	13
Journal	IEEE Transactions on Information Theory
Volume	62
Issue number	11
DOIs	https://doi.org/10.1109/TIT.2016.2609389
State	Published - 1 Nov 2016
Externally published	Yes

Keywords

Gilbert-Varshamov bound
Johnson bound
Multiply constant-weight codes
Plotkin bound
concatenation
graph decompositions
linear programming bound
skew almost-resolvable squares
spherical codes

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2016.2609389

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title = "New Bounds and Constructions for Multiply Constant-Weight Codes",

abstract = "Multiply constant-weight codes (MCWCs) were introduced recently to improve the reliability of certain physically unclonable function response. In this paper, the bounds of MCWCs and the constructions of optimal MCWCs are studied. First, we derive three different types of upper bounds which improve the Johnson-type bounds given by Chee et al. for some parameters. The asymptotic lower bound of MCWCs is also examined. Then, we obtain the asymptotic existence of two classes of optimal MCWCs, which shows that the Johnson-type bounds for MCWCs with distances 2 Σi=1m wi - 2 or 2mw - 2w are asymptotically exact. Finally, we construct a class of optimal MCWCs with total weight four and distance six by establishing the connection between such MCWCs and a new kind of combinatorial structures. As a consequence, the maximum sizes of MCWCs with total weight less than or equal to four are determined almost completely.",

keywords = "Gilbert-Varshamov bound, Johnson bound, Multiply constant-weight codes, Plotkin bound, concatenation, graph decompositions, linear programming bound, skew almost-resolvable squares, spherical codes",

author = "Xin Wang and Hengjia Wei and Chong Shangguan and Gennian Ge",

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year = "2016",

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doi = "10.1109/TIT.2016.2609389",

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T1 - New Bounds and Constructions for Multiply Constant-Weight Codes

AU - Wang, Xin

AU - Wei, Hengjia

AU - Shangguan, Chong

AU - Ge, Gennian

PY - 2016/11/1

Y1 - 2016/11/1

N2 - Multiply constant-weight codes (MCWCs) were introduced recently to improve the reliability of certain physically unclonable function response. In this paper, the bounds of MCWCs and the constructions of optimal MCWCs are studied. First, we derive three different types of upper bounds which improve the Johnson-type bounds given by Chee et al. for some parameters. The asymptotic lower bound of MCWCs is also examined. Then, we obtain the asymptotic existence of two classes of optimal MCWCs, which shows that the Johnson-type bounds for MCWCs with distances 2 Σi=1m wi - 2 or 2mw - 2w are asymptotically exact. Finally, we construct a class of optimal MCWCs with total weight four and distance six by establishing the connection between such MCWCs and a new kind of combinatorial structures. As a consequence, the maximum sizes of MCWCs with total weight less than or equal to four are determined almost completely.

AB - Multiply constant-weight codes (MCWCs) were introduced recently to improve the reliability of certain physically unclonable function response. In this paper, the bounds of MCWCs and the constructions of optimal MCWCs are studied. First, we derive three different types of upper bounds which improve the Johnson-type bounds given by Chee et al. for some parameters. The asymptotic lower bound of MCWCs is also examined. Then, we obtain the asymptotic existence of two classes of optimal MCWCs, which shows that the Johnson-type bounds for MCWCs with distances 2 Σi=1m wi - 2 or 2mw - 2w are asymptotically exact. Finally, we construct a class of optimal MCWCs with total weight four and distance six by establishing the connection between such MCWCs and a new kind of combinatorial structures. As a consequence, the maximum sizes of MCWCs with total weight less than or equal to four are determined almost completely.

KW - Gilbert-Varshamov bound

KW - Johnson bound

KW - Multiply constant-weight codes

KW - Plotkin bound

KW - concatenation

KW - graph decompositions

KW - linear programming bound

KW - skew almost-resolvable squares

KW - spherical codes

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DO - 10.1109/TIT.2016.2609389

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EP - 6327

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 11

M1 - 7567498

ER -

New Bounds and Constructions for Multiply Constant-Weight Codes

Abstract

Keywords

ASJC Scopus subject areas

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