The invertibility of the XOR of rotations of a binary word

On the invertibility of the XOR of rotations of a binary word

We prove the following result regarding operations on a binary word whose length is a power of two: computing the exclusive-or of a number of rotated versions of the word is an invertible (one-to-one) operation if and only if the number of versions combined is odd. (This result is not new; there is at least one earlier proof, due to Thomsen in his PhD thesis [12]. Our proof may be new.)

On the invertibility of the XOR rotations of a binary word

We prove the following result regarding operations on a binary word whose length is a power of two: computing the exclusive-or of a number of rotated versions of the word is an invertible (one-to-one) operation if and only if the number of versions combined is odd. (This result is not new; there is at least one earlier proof, due to Thomsen in his PhD thesis [12]. Our proof may be new.)

A Survey of Invertibility and Spectrum Preserving Linear Maps

Novel Defect Terminolgy Beside Evaluation And Design Fault Tolerant Logic Gates In Quantum-Dot Cellular Automata

Quantum dot Cellular Automata (QCA) is one of the important nano-level technologies for implementation of both combinational and sequential systems. QCA have the potential to achieve low power dissipation and operate high speed at THZ frequencies. However large probability of occurrence fabrication defects in QCA, is a fundamental challenge to use this emerging technology. Because of these vari...

A novel design for all-optical NAND/NOR/XOR gates based on nonlinear directional coupler

In this paper a novel all-optical logic NAND, NOR and XOR gate based on nonlinear directional coupler theory is demonstrated. We use the identical structure which contains three waveguides, for designing these gates; the only difference however, is the power of inputs light beam. In other words, while a beam with 4 W/μm in power considered as logical one, the output is NAND gate and if a beam w...