Upper bounds on matching families in BBZ{pq}^{n}

Upper bounds on matching families in BBZ{pq}^{n}

Matching families are one of the major ingredients in the construction of locally decodable codes (LDCs) and the best known constructions of LDCs with a constant number of queries are based on matching families. The determination of the largest size of any matching family in Zmn, where Zm is the rin...

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Main Authors: Chee, Yeow Meng, Ling, San, Wang, Huaxiong, Zhang, Liang Feng
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2013
Subjects:
DRNTU::Science::Mathematics
Online Access:https://hdl.handle.net/10356/101267
http://hdl.handle.net/10220/16778
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1012672020-03-07T12:37:12Z Upper bounds on matching families in BBZ{pq}^{n} Chee, Yeow Meng Ling, San Wang, Huaxiong Zhang, Liang Feng School of Physical and Mathematical Sciences DRNTU::Science::Mathematics Matching families are one of the major ingredients in the construction of locally decodable codes (LDCs) and the best known constructions of LDCs with a constant number of queries are based on matching families. The determination of the largest size of any matching family in Zmn, where Zm is the ring of integers modulo m, is an interesting problem. In this paper, we show an upper bound of O ((pq)0.625n+0.125) for the size of any matching family in Zpqn, where p and q are two distinct primes. Our bound is valid when n is a constant, p → ∞, and p/q → 1. Our result improves an upper bound of Dvir and coworkers. 2013-10-24T07:02:58Z 2019-12-06T20:35:49Z 2013-10-24T07:02:58Z 2019-12-06T20:35:49Z 2013 2013 Journal Article Chee, Y. M., Ling, S., Wang, H., & Zhang, L. F. (2013). Upper bounds on matching families in BBZ{pq}^{n}. IEEE transactions on information theory, 59(8), 5131-5139. 0018-9448 https://hdl.handle.net/10356/101267 http://hdl.handle.net/10220/16778 10.1109/TIT.2013.2257918 en IEEE transactions on information theory
institution Nanyang Technological University
building NTU Library
country Singapore
collection DR-NTU
language English
topic DRNTU::Science::Mathematics
spellingShingle DRNTU::Science::Mathematics
Chee, Yeow Meng
Ling, San
Wang, Huaxiong
Zhang, Liang Feng
Upper bounds on matching families in BBZ{pq}^{n}
description Matching families are one of the major ingredients in the construction of locally decodable codes (LDCs) and the best known constructions of LDCs with a constant number of queries are based on matching families. The determination of the largest size of any matching family in Zmn, where Zm is the ring of integers modulo m, is an interesting problem. In this paper, we show an upper bound of O ((pq)0.625n+0.125) for the size of any matching family in Zpqn, where p and q are two distinct primes. Our bound is valid when n is a constant, p → ∞, and p/q → 1. Our result improves an upper bound of Dvir and coworkers.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Chee, Yeow Meng
Ling, San
Wang, Huaxiong
Zhang, Liang Feng
format Article
author Chee, Yeow Meng
Ling, San
Wang, Huaxiong
Zhang, Liang Feng
author_sort Chee, Yeow Meng
title Upper bounds on matching families in BBZ{pq}^{n}
title_short Upper bounds on matching families in BBZ{pq}^{n}
title_full Upper bounds on matching families in BBZ{pq}^{n}
title_fullStr Upper bounds on matching families in BBZ{pq}^{n}
title_full_unstemmed Upper bounds on matching families in BBZ{pq}^{n}
title_sort upper bounds on matching families in bbz{pq}^{n}
publishDate 2013
url https://hdl.handle.net/10356/101267
http://hdl.handle.net/10220/16778
_version_ 1681042927013330944

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