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Codes. (English) Zbl 0854.94016

Colbourn, Charles J. (ed.) et al., The CRC handbook of combinatorial designs. Boca Raton, FL: CRC Press. CRC Press Series on Discrete Mathematics and its Applications. 517-543 (1996).
As usual for the CRC handbook of combinatorial designs, the author gives a survey of the most important facts in the area covered, coupled with many tables containing relevant information. In this case, the theme is the connection between designs and codes, and the individual topics covered are as follows (after an extremely brief introduction to coding theory): the construction of designs from the supports of the words of a given weight in a linear code (relation to perfect codes, Assmus-Mattson theorem); nonlinear codes and designs (e.g., applications to Preparata and Kerdock codes); majority decoding; designs, intersection numbers and codes (e.g., applications of coding theory to quasi-symmetric designs); the linear codes of Steiner triple systems; designs with the symmetric difference property (and their relations to difference sets and bent functions); maximal codes and Hadamard matrices; equidistant codes and orthogonal arrays; constant weight codes and designs.
For the entire collection see [Zbl 0836.00010].

MSC:

94B25 Combinatorial codes
94-02 Research exposition (monographs, survey articles) pertaining to information and communication theory
05-02 Research exposition (monographs, survey articles) pertaining to combinatorics
05B05 Combinatorial aspects of block designs
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