Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The capacity of $ C\sb{5}$ and free sets in $ C\sb{m}\sp{2}$


Authors: D. G. Mead and W. Narkiewicz
Journal: Proc. Amer. Math. Soc. 84 (1982), 308-310
MSC: Primary 20D60; Secondary 10L02, 94A15
MathSciNet review: 637189
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In a recent paper, S. K. Stein examined the problem of determining the cardinality, $ \tau (C_m^k)$, of the largest subset $ S$ of the direct product $ C_m^k$ of $ k$ copies of $ {C_m}$ such that distinct sums of elements of $ S$ yield distinct elements of $ C_m^k$. In this paper we show that $ {\tau ^* }({C_5}) = {\lim _{k \to \infty }}(\tau (C_5^k)/k) = 2$, answering a question raised by Stein. We also produce an infinite set of $ m$'s such that $ \tau (C_m^2) > 2[{\log _2}m]$.


References [Enhancements On Off] (What's this?)

  • [1] J.-P. Serre, A course in arithmetic, Springer-Verlag, New York-Heidelberg, 1973. Translated from the French; Graduate Texts in Mathematics, No. 7. MR 0344216
  • [2] Claude E. Shannon, The zero error capacity of a noisy channel, Institute of Radio Engineers, Transactions on Information Theory, IT-2 (1956), no. September, 8–19. MR 0089131
  • [3] S. K. Stein, Modified linear dependence and the capacity of a cyclic graph, Linear Algebra and Appl. 17 (1977), no. 3, 191–195. MR 0463019

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20D60, 10L02, 94A15

Retrieve articles in all journals with MSC: 20D60, 10L02, 94A15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0637189-4
Article copyright: © Copyright 1982 American Mathematical Society