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Kernels of nonlinear Hamming codes

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Abstract

Given a binary code,C, of lengthn, thekernel of the code is defined to be the set of all vectors which leave the code invariant under translation. Throughout this paper, various properties of kernels will be considered. However, the main idea of this paper is to show the necessary and sufficient conditions for the existence of kernels of all possible sizes for nonlinear perfect binary codes.

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Authors and Affiliations

  1. Department of Discrete and Statistical Sciences, Auburn University, 120 Math Annex, 36849-5307, Auburn, Alabama, USA

    Kevin T. Phelps & Mike Levan

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  1. Kevin T. Phelps
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  2. Mike Levan
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Communicated by: R. Mullin

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Phelps, K.T., Levan, M. Kernels of nonlinear Hamming codes. Des Codes Crypt 6, 247–257 (1995). https://doi.org/10.1007/BF01388478

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  • DOI: https://doi.org/10.1007/BF01388478

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