Abstract
There are great many non linear codes and we can hope to find some of them that fill the space much more than linear codes do. The Preparata codes, for example, contain twice as many codewords as the double-error-correcting BCH code of the same length: they are optimal codes, i. e. they have the largest possible number of codewords for given length and distance.
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References
Goethals J. M. “Two dual families of nonlinear binary codes” Electronics Letters, 10, 471 (1974).
Goethals J.M. and Snover S.L.: “Nearly perfect binary codes” Discrete Mathematics, 3, 65 (1972).
Mac Williams J., Sloane N., and Goethals J.M.: “The Mac Williams identities for nonlinear codes” Bell System Tech. J., 51, 803 (1972).
Preparata F.: “A class of optimum nonlinear double error correcting codes” Information and Control, 13, 378 (1968).
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© 1975 Springer-Verlag Wien
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Huberman, A., Chouchan, A. (1975). Preparata Codes and Goethals’ Generalization: The Dual of a Nonlinear Code. In: Longo, G. (eds) Information Theory New Trends and Open Problems. International Centre for Mechanical Sciences, vol 219. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2730-8_12
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DOI: https://doi.org/10.1007/978-3-7091-2730-8_12
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-81378-2
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