Fourier Codes and Hartley Codes
Information Theory
2015-02-10 v1 math.IT
Abstract
Real-valued block codes are introduced, which are derived from Discrete Fourier Transforms (DFT) and Discrete Hartley Transforms (DHT). These algebraic structures are built from the eigensequences of the transforms. Generator and parity check matrices were computed for codes up to block length N=24. They can be viewed as lattices codes so the main parameters (dimension, minimal norm, area of the Voronoi region, density, and centre density) are computed. Particularly, Hamming-Hartley and Golay-Hartley block codes are presented. These codes may possibly help an efficient computation of a DHT/DFT.
Keywords
Cite
@article{arxiv.1502.02489,
title = {Fourier Codes and Hartley Codes},
author = {H. M. de Oliveira and C. M. F. Barros and R. M. Campello de Souza},
journal= {arXiv preprint arXiv:1502.02489},
year = {2015}
}
Comments
5 pages, 4 tables, 1 appedix. conference: XXV Simposio Brasileiro de Telecomunicacoes, SBrT'07, Recife, PE, Brazil, 2007