In earlier papers the author developed upper bounds for A(n, d), the maximum number of binary words of length n, each pair of words being at a Hamming distance of at least d apart. These sphere packing bounds for A(n, d) depend directly on a related bound for constant weight codes where each word has the same number of 1's. Improving bounds on constant weight codes would therefore improve the bounds on A(n, d). This was the motivation of this report, but constant weight codes are interesting in their own right. By combining special techniques from several sources, a new upper bound for constant weight codes is developed which gives significantly improved results.
This report is part of the RAND Corporation Report series. The report was a product of the RAND Corporation from 1948 to 1993 that represented the principal publication documenting and transmitting RAND's major research findings and final research.
Our mission to help improve policy and decisionmaking through research and analysis is enabled through our core values of quality and objectivity and our unwavering commitment to the highest level of integrity and ethical behavior. To help ensure our research and analysis are rigorous, objective, and nonpartisan, we subject our research publications to a robust and exacting quality-assurance process; avoid both the appearance and reality of financial and other conflicts of interest through staff training, project screening, and a policy of mandatory disclosure; and pursue transparency in our research engagements through our commitment to the open publication of our research findings and recommendations, disclosure of the source of funding of published research, and policies to ensure intellectual independence. For more information, visit www.rand.org/about/principles.
The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.