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...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2013
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| Online Access: | https://hdl.handle.net/10356/96425 http://hdl.handle.net/10220/9840 |
| _version_ | 1811689490675138560 |
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| author | Fu, Fang-Wei Ling, San Xing, Chaoping |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Fu, Fang-Wei Ling, San Xing, Chaoping |
| author_sort | Fu, Fang-Wei |
| collection | NTU |
| 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. |
| first_indexed | 2024-10-01T05:48:56Z |
| format | Journal Article |
| id | ntu-10356/96425 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:48:56Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-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 |
| 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 |
| title | 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_short | 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 |
| topic | DRNTU::Science::Mathematics::Discrete mathematics |
| url | https://hdl.handle.net/10356/96425 http://hdl.handle.net/10220/9840 |
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