New code upper bounds for the folded n-cube

Lihang Hou; Bo Hou; Suogang Gao; Wei Hsuan Yu

doi:10.1016/j.jcta.2019.105182

New code upper bounds for the folded n-cube

Lihang Hou, Bo Hou, Suogang Gao, Wei Hsuan Yu

Department of Mathematics

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

4 Scopus citations

Abstract

Let □_n denote the folded n-cube and let A(□_n,d) denote the maximum size of a code in □_n with minimum distance at least d. We give an upper bound on A(□_n,d) based on block-diagonalizing the Terwilliger algebra of □_n and on semidefinite programming. The technique of this paper is an extension of the approach taken by A. Schrijver [11] on the study of upper bounds for binary codes.

Original language	English
Article number	105182
Journal	Journal of Combinatorial Theory. Series A
Volume	172
DOIs	https://doi.org/10.1016/j.jcta.2019.105182
State	Published - May 2020

Keywords

Code
Semidefinite programming
Terwilliger algebra
Upper bounds

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10.1016/j.jcta.2019.105182

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title = "New code upper bounds for the folded n-cube",

abstract = "Let □n denote the folded n-cube and let A(□n,d) denote the maximum size of a code in □n with minimum distance at least d. We give an upper bound on A(□n,d) based on block-diagonalizing the Terwilliger algebra of □n and on semidefinite programming. The technique of this paper is an extension of the approach taken by A. Schrijver [11] on the study of upper bounds for binary codes.",

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AU - Hou, Lihang

AU - Hou, Bo

AU - Gao, Suogang

AU - Yu, Wei Hsuan

PY - 2020/5

Y1 - 2020/5

N2 - Let □n denote the folded n-cube and let A(□n,d) denote the maximum size of a code in □n with minimum distance at least d. We give an upper bound on A(□n,d) based on block-diagonalizing the Terwilliger algebra of □n and on semidefinite programming. The technique of this paper is an extension of the approach taken by A. Schrijver [11] on the study of upper bounds for binary codes.

AB - Let □n denote the folded n-cube and let A(□n,d) denote the maximum size of a code in □n with minimum distance at least d. We give an upper bound on A(□n,d) based on block-diagonalizing the Terwilliger algebra of □n and on semidefinite programming. The technique of this paper is an extension of the approach taken by A. Schrijver [11] on the study of upper bounds for binary codes.

KW - Code

KW - Semidefinite programming

KW - Terwilliger algebra

KW - Upper bounds

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JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

M1 - 105182

ER -

New code upper bounds for the folded n-cube

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Keywords

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