A linear construction for certain Kerdock and Preparata codes
<|reference_start|>A linear construction for certain Kerdock and Preparata codes: The Nordstrom-Robinson, Kerdock, and (slightly modified) Pre\- parata codes are shown to be linear over $\ZZ_4$, the integers $\bmod~4$. The Kerdock and Preparata codes are duals over $\ZZ_4$, and the Nordstrom-Robinson code is self-dual. All these codes are just extended cyclic codes over $\ZZ_4$. 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 $\ZZ_4$, but Hamming codes in general are not, nor is the Golay code.<|reference_end|>
@article{calderbank1993a,
    title={A linear construction for certain Kerdock and Preparata codes},
    author={A. R. Calderbank, A. Roger Hammons Jr., P. Vijay Kumar, N. J. A.
  Sloane, Patrick Sol'e},
    journal={Bull. Amer. Math. Soc. (N.S.) 29 (1993) 218-222},
    year={1993},
    number={Bulletin migration 11/99},
    archivePrefix={arXiv},
    eprint={math/9310227},
    primaryClass={math.CO cs.IT math.IT}
}