Conditions of the Affine Extension of an Incompletely Defined Boolean Function
keywords: Walsh coefficients, coefficients distribution, incompletely defined Boolean function, affine function
The paper presents conditions of extension of the weakly defined Boolean functions to their full affine form. The main goal of the analysis is a fast estimation whether a given incompletely defined function can be extended to a full affine form. If it is possible a simple algorithm of the states completion has been proposed. In such a case undefined points are clearly replaced by 0, 1 values. Spectral coefficients of a Boolean function allow to determine whether a partially defined function can be realised as affine.
mathematics subject classification 2000: 06E30, 94C10, 43A32
reference: Vol. 29, 2010, No. 6+, pp. 1073–1088
