27 citations · 229 across the 64 of their papers we have counts for
15 papers · 1 filter
Geometrical Representation for Number-theoretic Transforms
H. M. de Oliveira, R. J. Cintra
This short note introduces a geometric representation for binary (or ternary) sequences. The proposed representation is linked to multivariate data plotting according to the radar…
A Note on the Shannon Entropy of Short Sequences
H. M. de Oliveira, Raydonal Ospina
For source sequences of length L symbols we proposed to use a more realistic value to the usual benchmark of number of code letters by source letters. Our idea is based on a quanti…
The Hamming and Golay Number-Theoretic Transforms
A. J. A. Paschoal, R. M. Campello de Souza, H. M. de Oliveira
New number-theoretic transforms are derived from known linear block codes over finite fields. In particular, two new such transforms are built from perfect codes, namely the \texti…
Multiuser Communication Based on the DFT Eigenstructure
R. M. Campello de Souza, H. M. de Oliveira, R. J. Cintra
The eigenstructure of the discrete Fourier transform (DFT) is examined and new systematic procedures to generate eigenvectors of the unitary DFT are proposed. DFT eigenvectors are…
Efficient Multiplex for Band-Limited Channels: Galois-Field Division Multiple Access
H. M. de Oliveira, R. M. Campello de Souza, A. N. Kauffman
A new Efficient-bandwidth code-division-multiple-access (CDMA) for band-limited channels is introduced which is based on finite field transforms. A multilevel code division multipl…
Shannon and Renyi Entropy of Wavelets
H. M. de Oliveira
This paper reports a new reading for wavelets, which is based on the classical 'De Broglie' principle. The wave-particle duality principle is adapted to wavelets. Every continuous…
Quantum Decoding with Venn Diagrams
C. M. F. Barros, Francisco Marcos de Assis, H. M. de Oliveira
The quantum error correction theory is as a rule formulated in a rather convoluted way, in comparison to classical algebraic theory. This work revisits the error correction in a no…
Fourier Codes
R. M. Campello de Souza, E. S. V. Freire, H. M. de Oliveira
A new family of error-correcting codes, called Fourier codes, is introduced. The code parity-check matrix, dimension and an upper bound on its minimum distance are obtained from th…
Orthogonal Multilevel Spreading Sequence Design
H. M. de Oliveira, R. M. Campello de Souza
Finite field transforms are offered as a new tool of spreading sequence design. This approach exploits orthogonality properties of synchronous non-binary sequences defined over a c…
Wavelet Analysis as an Information Processing Technique
H. M. de Oliveira, D. F. de Souza
A new interpretation for the wavelet analysis is reported, which can is viewed as an information processing technique. It was recently proposed that every basic wavelet could be as…
Spread-Spectrum Based on Finite Field Fourier Transforms
H. M. de Oliveira, J. P. C. L. Miranda, R. M. Campello de Souza
Spread-spectrum systems are presented, which are based on Finite Field Fourier Transforms. Orthogonal spreading sequences defined over a finite field are derived. New digital multi…
On Galois-Division Multiple Access Systems: Figures of Merit and Performance Evaluation
J. P. C. L. Miranda, H. M. de Oliveira
A new approach to multiple access based on finite field transforms is investigated. These schemes, termed Galois-Division Multiple Access (GDMA), offer compact bandwidth requiremen…
Multiresolution Division Multiplex (MRDM): A New Wavelet-based Multiplex System
H. M. de Oliveira, E. A. Bouton
An original multiplex scheme is introduced, which is based on Mallat's multiresolution formulation of wavelet systems. This system is adaptable and its implementation is well match…
Fourier Codes and Hartley Codes
H. M. de Oliveira, C. M. F. Barros, R. M. Campello de Souza
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 th…
On Wavelet Decomposition over Finite Fields
H. M. de Oliveira, T. H. Falk
This paper introduces some foundations of wavelets over Galois fields. Standard orthogonal finite-field wavelets (FF-Wavelets) including FF-Haar and FF-Daubechies are derived. Non-…