A linear construction for certain Kerdock and Preparata codes
Combinatorics
2009-09-25 v1 Information Theory
math.IT
Abstract
The Nordstrom-Robinson, Kerdock, and (slightly modified) Pre\- parata codes are shown to be linear over , the integers . The Kerdock and Preparata codes are duals over , and the Nordstrom-Robinson code is self-dual. All these codes are just extended cyclic codes over . 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 , but Hamming codes in general are not, nor is the Golay code.
Keywords
Cite
@article{arxiv.math/9310227,
title = {A linear construction for certain Kerdock and Preparata codes},
author = {A. R. Calderbank and A. Roger Hammons and P. Vijay Kumar and N. J. A. Sloane and Patrick Solé},
journal= {arXiv preprint arXiv:math/9310227},
year = {2009}
}
Comments
5 pages