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The Sizes of Optimal $q$-Ary Codes of Weight Three and Distance Four: A Complete Solution

2008; Institute of Electrical and Electronics Engineers; Volume: 54; Issue: 3 Linguagem: Inglês

10.1109/tit.2007.915885

1557-9654

Yeow Meng Chee, Son Hoang Dau, Alan C. H. Ling, San Ling,

Cooperative Communication and Network Coding

In Theorem III.2, the existence of networks that achieve prescribed rational-valued node-limited capacity functions was established.It is known in general that not all networks necessarily achieve their capacities [5].It is presently unknown, however, whether a network coding capacity could be irrational. 5Thus, we are not presently able to extend Theorem III.2 to real-valued functions.Nevertheless, Theorem III.2 does immediately imply the following asymptotic achievability result for real-valued functions.Corollary III.5:Every monotonically nondecreasing, eventually