BibTeX
@MISC{Udaya98decodingof,
author = {P. Udaya and Alexis Bonnecaze},
title = {Decoding of Cyclic Codes over . . .},
year = {1998}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
We give a simple decoding algorithm to decode linear cyclic codes of odd length over the ring R = F2 + uF2 = f0; 1; u; u = u + 1g, where u 2 = 0. A spectral representation of the cyclic codes over R is given and a BCH like bound is given for the Lee distance of the codes. The ring R shares many properties of Z4 and F4 and admits a linear "Gray map". Keywords: Codes over rings, Cyclic codes, Self-dual codes, Gray map. Acknowledgement: Udaya P. acknowledges the support of Australian Research Council Large Grant #A49701206. 2 0 1 u u 0 0 0 0 0 1 0 1 u u u 0 u 1 u u 0 u u 0 + 0 1 u u 0 0 1 u u 1 1 0 u u u u u 0 1 u u u 1 0 Table 1: Multiplication and addition tables for the ring F 2 + F 2 . 1 Introduction Codes over rings have recently received a large deal of interest among coding theorists. Ring theory, as predicted earlier by McDonald [10], offers a general setting to define and study codes. The most recent success was with the ring of integers modulo four, Z 4 , which expl...
