A Linear Construction for Certain Kerdock and Preparata Codes
Authors: A.R.Calderbank, A.R.Hammons, Jr., P. Vijay Kumar,
N. J. A. Sloane, and Patrick Sole
ABSTRACT
The Nordstrom-Robinson, Kerdock and (slightly modified) Preparata codes are
shown to be linear over Z sub 4, the integers mod 4.
The Kerdock and Preparata codes are duals over Z sub 4,
and the Nordstrom-Robinson code is self-dual.
All these codes are just extended cyclic codes over Z sub 4 .
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
Z sub 4 , but Hamming codes in general are not,
nor is the Golay code.
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