Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.dam.2004.08.004
Title: On the variance of average distance of subsets in the Hamming space
Authors: Fu, F.-W. 
Ling, S. 
Xing, C. 
Keywords: Average distance
Codes
Distance distribution
Hamming space
Subsets
Variance
Issue Date: 30-Jan-2005
Citation: Fu, F.-W., Ling, S., Xing, C. (2005-01-30). On the variance of average distance of subsets in the Hamming space. Discrete Applied Mathematics 145 (3) : 465-478. ScholarBank@NUS Repository. https://doi.org/10.1016/j.dam.2004.08.004
Abstract: 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 Vn 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. © 2004 Elsevier B.V. All rights reserved.
Source Title: Discrete Applied Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/111456
ISSN: 0166218X
DOI: 10.1016/j.dam.2004.08.004
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