Please use this identifier to cite or link to this item: https://doi.org/10.1007/s10623-007-9049-6
Title: The characterization of binary constant weight codes meeting the bound of Fu and Shen
Authors: Fu, F.-W. 
Xia, S.-T.
Keywords: Binary codes
Binary constant weight codes
Distance distribution
Grey-Rankin boundm
Quasi-symmetric designs
Issue Date: Apr-2007
Citation: Fu, F.-W., Xia, S.-T. (2007-04). The characterization of binary constant weight codes meeting the bound of Fu and Shen. Designs, Codes, and Cryptography 43 (1) : 9-20. ScholarBank@NUS Repository. https://doi.org/10.1007/s10623-007-9049-6
Abstract: Fu and Shen gave an upper bound on binary constant weight codes. In this paper, we present a new proof for the bound of Fu and Shen and characterize binary constant weight codes meeting this bound. It is shown that binary constant weight codes meet the bound of Fu and Shen if and only if they are generated from certain symmetric designs and quasi-symmetric designs in combinatorial design theory. In particular, it turns out that the existence of binary codes with even length meeting the Grey-Rankin bound is equivalent to the existence of certain binary constant weight codes meeting the bound of Fu and Shen. Furthermore, some examples are listed to illustrate these results. Finally, we obtain a new upper bound on binary constant weight codes which improves on the bound of Fu and Shen in certain case. © Springer Science+Business Media, LLC 2007.
Source Title: Designs, Codes, and Cryptography
URI: http://scholarbank.nus.edu.sg/handle/10635/111493
ISSN: 09251022
DOI: 10.1007/s10623-007-9049-6
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