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 ℤ4, the integers mod 4. 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. © 1993 American Mathematical Society.
Calderbank, AR; Hammons, AR; Kumar, PV; Sloane, NJA; Solé, P
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