A linear construction for certain kerdock and preparata codes

Journal Article (Journal)

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.

Full Text

Duke Authors

Cited Authors

  • Calderbank, AR; Hammons, AR; Kumar, PV; Sloane, NJA; Solé, P

Published Date

  • January 1, 1993

Published In

Volume / Issue

  • 29 / 2

Start / End Page

  • 218 - 222

International Standard Serial Number (ISSN)

  • 0273-0979

Digital Object Identifier (DOI)

  • 10.1090/S0273-0979-1993-00426-9

Citation Source

  • Scopus