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Games and codes. (English) Zbl 0742.90104

Combinatorial games, Lect. Notes AMS Short Course, Columbus/OH (USA) 1990, Proc. Symp. Appl. Math. 43, 101-110 (1991).
[For the entire collection see Zbl 0721.00028.]
This paper gives basic concepts in coding needed to explain how certain binary codes are lexicodes. Lexicodes are described by J. H. Conway and N. J. A. Sloane [IEEE Trans. Inf. Theory IT-32, 337-348 (1986; Zbl 0594.94023)] as codes whose codewords are the winning positions in particular combinatorial games. Explicit examples of this connection are given for coin turning games and Hamming codes, and some quadratic residue codes. Open problems and relations to combinatorial designs are given.
Reviewer: V.Pless

MSC:

91A46 Combinatorial games
91A05 2-person games
94B25 Combinatorial codes
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