Math @ Duke

Publications [#235822] of Robert Calderbank
Papers Published
 Calderbank, AR; Mcguire, G, Construction of a (64,2^{37},12) Code via Galois Rings,
Designs, Codes, and Cryptography, vol. 10 no. 2
(1997),
pp. 157165
(last updated on 2017/12/11)
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 NordstromRobinson 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 NordstromRobinson code is defined in this same way, and like the NordstromRobinson code, the new code is better than any linear code that is presently known.


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