Displaying similar documents to “Efficient calculation of the Reed-Muller form by means of the Walsh transform”

The spectral test of the Boolean function linearity

Piotr Porwik (2003)

International Journal of Applied Mathematics and Computer Science

Similarity:

The paper discusses the problem of recognizing the Boolean function linearity. A spectral method of the analysis of Boolean functions using the Walsh transform is described. Linearity and nonlinearity play important roles in the design of digital circuits. The analysis of the distribution of spectral coefficients allows us to determine various combinatorial properties of Boolean functions, such as redundancy, monotonicity, self-duality, correcting capability, etc., which seems more difficult...

Dedicated spectral method of Boolean function decomposition

Piotr Porwik, Radomir Stankovic (2006)

International Journal of Applied Mathematics and Computer Science

Similarity:

Spectral methods constitute a useful tool in the analysis and synthesis of Boolean functions, especially in cases when other methods reduce to brute-force search procedures. There is renewed interest in the application of spectral methods in this area, which extends also to the closely connected concept of the autocorrelation function, for which spectral methods provide fast calculation algorithms. This paper discusses the problem of spectral decomposition of Boolean functions using...

Algorithms for Computing the Linearity and Degree of Vectorial Boolean Functions

Bouyuklieva, Stefka, Bouyukliev, Iliya (2016)

Serdica Journal of Computing

Similarity:

In this article, we study two representations of a Boolean function which are very important in the context of cryptography. We describe Möbius and Walsh Transforms for Boolean functions in details and present effective algorithms for their implementation. We combine these algorithms with the Gray code to compute the linearity, nonlinearity and algebraic degree of a vectorial Boolean function. Such a detailed consideration will be very helpful for students studying the design of block...

WWW-based Boolean function minimization

Sebastian Tomaszewski, Ilgaz Celik, George Antoniou (2003)

International Journal of Applied Mathematics and Computer Science

Similarity:

In this paper a Boolean minimization algorithm is considered and implemented as an applet in Java. The application is based on the Quine-McCluskey simplification technique with some modifications. The given application can be accessed on line since it is posted on the World Wide Web (WWW), with up to four variables, at the URL http://www.csam.montclair.edu/~antoniou/bs. After extensive testing, the performance of the algorithm has been found to be excellent. The proposed application...

On Boolean modus ponens.

Sergiu Rudeanu (1998)

Mathware and Soft Computing

Similarity:

An abstract form of modus ponens in a Boolean algebra was suggested in [1]. In this paper we use the general theory of Boolean equations (see e.g. [2]) to obtain a further generalization. For a similar research on Boolean deduction theorems see [3].