Kittens, Mathematical Blackjack, and Combinatorial Codes

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


Can coding theory help you be a better gambler? Do unexpected combinatorial patterns (called Steiner systems) arise naturally in codes? This chapter attempts to address these types of questions. (The books by Assmus and Key (Designs and Codes. Cambridge University Press, Cambridge, 1992) and Conway and Sloane (Sphere Packings, Lattices and Groups, 3rd edn. Springer, Berlin, 1999) do into more detail in these matters and are highly recommended.)

This chapter gives an exposition of some ideas of Hadamard and Mathieu, as well as ideas of Conway, Curtis, and Ryba connecting the Steiner system S(5,6,12) with a card game called mathematical blackjack. An implementation in SAGE is described as well. Then we turn to one of the most beautiful results in coding theory, the Assmus–Mattson Theorem, which relates certain linear codes to combinatorial structures called designs. Finally, we describe an old scheme for placing bets using Golay codes (the scheme was in fact published in a Finnish soccer magazine years before the error-correcting code itself was discovered (Hämäläinen et al., Am. Math. Mon. 102:579–588, 1995)).

Open questions which arise in this chapter include conjectures on Hadamard matrices and on which block designs “arise” from an error-correcting code.


Orthogonal Array Linear Code Winning Strategy Hadamard Matrice Hadamard Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Mathematics DepartmentUS Naval AcademyAnnapolisUSA
  2. 2.Department of MathematicsUniversity of LouisvilleLouisvilleUSA

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