Berlekamp switching game

The Berlekamp switching game is a mathematical game proposed by American mathematician Elwyn Berlekamp.[1] It has also been called the Gale–Berlekamp switching game, after David Gale, who discovered the same game independently,[2] or the unbalancing lights game.[3] It involves a system of lightbulbs controlled by two banks of switches, with one game player trying to turn many lightbulbs on and the other trying to keep as many as possible off. It can be used to demonstrate the concept of covering radius in coding theory.

  1. ^ Sloane, N. J. A. (1987). "Unsolved problems related to the covering radius of codes". In Cover, Thomas M.; Gopinath, B. (eds.). Open Problems in Communication and Computation. New York: Springer. pp. 51–56. doi:10.1007/978-1-4612-4808-8_11.
  2. ^ Spencer, Joel (1994). "Lecture 6: Chaos from order". Ten Lectures on the Probabilistic Method. CBMS-NSF Regional Conference Series in Applied Mathematics. Vol. 64 (Second ed.). Philadelphia, Pennsylvania: Society for Industrial and Applied Mathematics. pp. 45–50. doi:10.1137/1.9781611970074. ISBN 0-89871-325-0. MR 1249485.
  3. ^ Araújo, Gustavo; Pellegrino, Daniel (2019). "A Gale–Berlekamp permutation-switching problem in higher dimensions". European Journal of Combinatorics. 77: 17–30. arXiv:1801.09194. doi:10.1016/j.ejc.2018.10.007. MR 3872901. S2CID 57760841.