A linear construction for certain Kerdock and Preparata codes-Reference-Cited by-同舟云学术

A linear construction for certain Kerdock and Preparata codes

Published:1993 Issue:2 Volume:29 Page:218-222
ISSN:0273-0979
Container-title:Bulletin of the American Mathematical Society
language:en
Short-container-title:Bull. Amer. Math. Soc.

Author:

Calderbank A. R.,Hammons A. R.,Kumar P. Vijay,Sloane N. J. A.,Solé Patrick

Abstract

The Nordstrom-Robinson, Kerdock, and (slightly modified) Preparata codes are shown to be linear over Z 4 {\mathbb {Z}_4} , the integers mod 4 {\bmod \;4} . The Kerdock and Preparata codes are duals over Z 4 {\mathbb {Z}_4} , and the Nordstrom-Robinson code is self-dual. All these codes are just extended cyclic codes over Z 4 {\mathbb {Z}_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 4 {\mathbb {Z}_4} , but Hamming codes in general are not, nor is the Golay code.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/bull/1993-29-02/S0273-0979-1993-00426-9/S0273-0979-1993-00426-9.pdf

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