A linear construction for certain Kerdock and Preparata codes

Calderbank, A. R. ; Hammons, A. R. ; Vijay Kumar, P. ; Sloane, N. J. A. ; Sole, Patrick (1993) A linear construction for certain Kerdock and Preparata codes Bulletin of the American Mathematical Society, 29 (2). pp. 218-223. ISSN 0273-0979

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Official URL: http://www.ams.org/journals/bull/1993-29-02/S0273-...

Related URL: http://dx.doi.org/10.1090/S0273-0979-1993-00426-9


The Nordstrom-Robinson, Kerdock, and (slightly modified) Preparata codes are shown to be linear over Z4, the integers mod4. The Kerdock and Preparata codes are duals over Z4, and the Nordstrom-Robinson code is self-dual. All these codes are just extended cyclic codes over Z4. This provides a simple definition for these codes and explains why their Hamming weight distributions are dual to each other. First- and second-order Reed-Muller codes are also linear codes over Z4, but Hamming codes in general are not, nor is the Golay code.

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