On the variance of average distance of subsets in the Hamming space

Let V be a finite set with q distinct elements. For a subset C of V n, denote var(C) the variance of the average Hamming distance of C. Let T (n,M; q) and R(n,M; q) denote the minimum and maximum variance of the average Hamming distance of subsets of V n with cardinality M, respectively. In this pa...

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Main Authors:	Fu, Fang-Wei, Ling, San, Xing, Chaoping
Other Authors:	School of Physical and Mathematical Sciences
Format:	Article
Language:	English
Published:	2013
Subjects:	DRNTU::Science::Mathematics::Discrete mathematics
Online Access:	https://hdl.handle.net/10356/96425 http://hdl.handle.net/10220/9840
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Institution:	Nanyang Technological University
Language:	English

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spelling	sg-ntu-dr.10356-964252023-02-28T19:22:51Z On the variance of average distance of subsets in the Hamming space Fu, Fang-Wei Ling, San Xing, Chaoping School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Discrete mathematics Let V be a finite set with q distinct elements. For a subset C of V n, denote var(C) the variance of the average Hamming distance of C. Let T (n,M; q) and R(n,M; q) denote the minimum and maximum variance of the average Hamming distance of subsets of V n with cardinality M, respectively. In this paper, we study T (n,M; q) and R(n,M; q) for general q. Using methods from coding theory, we derive upper and lower bounds on var(C), which generalize and unify the bounds for the case q = 2. These bounds enable us to determine the exact value for T (n,M; q) and R(n,M; q) in several cases. Accepted version 2013-04-18T09:06:19Z 2019-12-06T19:30:33Z 2013-04-18T09:06:19Z 2019-12-06T19:30:33Z 2004 2004 Journal Article Fu, F. W., Ling, S., & Xing, C. (2004). On the variance of average distance of subsets in the Hamming space. Discrete Applied Mathematics, 145(3), 465-478. 0166218X https://hdl.handle.net/10356/96425 http://hdl.handle.net/10220/9840 10.1016/j.dam.2004.08.004 en Discrete applied mathematics © 2004 Elsevier B.V. This is the author created version of a work that has been peer reviewed and accepted for publication by Discrete Applied Mathematics, Elsevier B.V. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1016/j.dam.2004.08.004]. application/pdf
institution	Nanyang Technological University
building	NTU Library
continent	Asia
country	Singapore Singapore
content_provider	NTU Library
collection	DR-NTU
language	English
topic	DRNTU::Science::Mathematics::Discrete mathematics
spellingShingle	DRNTU::Science::Mathematics::Discrete mathematics Fu, Fang-Wei Ling, San Xing, Chaoping On the variance of average distance of subsets in the Hamming space
description	Let V be a finite set with q distinct elements. For a subset C of V n, denote var(C) the variance of the average Hamming distance of C. Let T (n,M; q) and R(n,M; q) denote the minimum and maximum variance of the average Hamming distance of subsets of V n with cardinality M, respectively. In this paper, we study T (n,M; q) and R(n,M; q) for general q. Using methods from coding theory, we derive upper and lower bounds on var(C), which generalize and unify the bounds for the case q = 2. These bounds enable us to determine the exact value for T (n,M; q) and R(n,M; q) in several cases.
author2	School of Physical and Mathematical Sciences
author_facet	School of Physical and Mathematical Sciences Fu, Fang-Wei Ling, San Xing, Chaoping
format	Article
author	Fu, Fang-Wei Ling, San Xing, Chaoping
author_sort	Fu, Fang-Wei
title	On the variance of average distance of subsets in the Hamming space
title_short	On the variance of average distance of subsets in the Hamming space
title_full	On the variance of average distance of subsets in the Hamming space
title_fullStr	On the variance of average distance of subsets in the Hamming space
title_full_unstemmed	On the variance of average distance of subsets in the Hamming space
title_sort	on the variance of average distance of subsets in the hamming space
publishDate	2013
url	https://hdl.handle.net/10356/96425 http://hdl.handle.net/10220/9840
_version_	1759855885997309952

On the variance of average distance of subsets in the Hamming space

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