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Construction of a (64, 2 37, 12) Code via Galois Rings

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Abstract

Certain nonlinear binary codes contain more codewords than any comparable linear code presently known. These include the Kerdock and Preparata codes, which exist for all lengths 4m ≥ 16. At length 16 they coincide to give the Nordstrom-Robinson code. This paper constructs a nonlinear (64, 237, 12) code as the binary image, under the Gray map, of an extended cyclic code defined over the integers modulo 4 using Galois rings. The Nordstrom-Robinson code is defined in this same way, and like the Nordstrom-Robinson code, the new code is better than any linear code that is presently known.

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Authors
  1. A. R. Calderbank
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  2. Gary McGuire
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Calderbank, A.R., McGuire, G. Construction of a (64, 2 37, 12) Code via Galois Rings. Designs, Codes and Cryptography 10, 157–165 (1997). https://doi.org/10.1023/A:1008240319733

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  • DOI: https://doi.org/10.1023/A:1008240319733

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