Patterson-Wiedemann type functions on 21 variables with Nonlinearity greater than Bent Concatenation bound

Nonlinearity is one of the most challenging combinatorial property in the domain of Boolean function research. Obtaining nonlinearity greater than the bent concatenation bound for odd number of variables continues to be one of the most sought after combinatorial research problems. The pioneering result in this direction has been discovered by Patterson and Wiedemann in 1983 (IEEE-IT), which considered Boolean functions on $5 \times 3 = 15$ variables that are invariant under the actions of the cyclic group ${GF(2^5)}^\ast \cdot {GF(2^3)}^\ast$ as well as the group of Frobenius authomorphisms. Some of these Boolean functions posses nonlinearity greater than the bent concatenation bound. The next possible option for exploring such functions is on $7 \times 3 = 21$ variables. However, obtaining such functions remained elusive for more than three decades even after substantial efforts as evident in the literature. In this paper, we exploit combinatorial arguments together with heuristic search to demonstrate such functions for the first time

Fast generation and covering radius of Reed-Muller Codes

Reed-Muller codes are known to be some of the oldest, simplest and most elegant error correcting codes. Reed-Muller codes were invented in 1954 by D. E. Muller and I. S. Reed, and were an important extension of the Hamming and Golay codes because they gave more flexibility in the size of the codeword and the number of errors that could be correct. The covering radius of these codes, as well as the fast construction of covering codes, is the main subject of this thesis. The covering radius problem is important because of the problem of constructing codes having a specified length and dimension. Codes with a reasonably small covering radius are highly desired in digital communication environments. In addition, a new algorithm is presented that allows the use of a compact way to represent Reed-Muller codes. Using this algorithm, a new method for fast, less complex, and memory efficient generation of 1st and 2nd order Reed - Muller codes and their hardware implementation is possible. It is also allows the fast construction of a new subcode class of 2nd order Reed-Muller codes with good properties. Finally, by reversing this algorithm, we introduce a code compression method, and at the same time a fast, efficient, and promising error-correction process.http://archive.org/details/fastgenerationnd109454471Hellenic Army author

Recent Development of Hybrid Renewable Energy Systems

Abstract: The use of renewable energies continues to increase. However, the energy obtained from renewable resources is variable over time. The amount of energy produced from the renewable energy sources (RES) over time depends on the meteorological conditions of the region chosen, the season, the relief, etc. So, variable power and nonguaranteed energy produced by renewable sources implies intermittence of the grid. The key lies in supply sources integrated to a hybrid system (HS)