Concepts inAlgorithm 823: Implementing scrambled digital sequences
Sobol sequence
Sobol sequences (also called LPτ sequences or sequences in base 2) are an example of quasi-random low-discrepancy sequences. They were first introduced by the Russian mathematician I. M. Sobol (Илья Меерович Соболь) in 1967. These sequences use a base of two to form successively finer uniform partitions of the unit interval, and then reorder the coordinates in each dimension.
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Sequence
In mathematics, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements), and the number of ordered element (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. A sequence is a discrete function. For example, (C, R, Y) is a sequence of letters that differs from (Y, C, R), as the ordering matters.
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Root mean square
In mathematics, the root mean square (abbreviated RMS or rms), also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g. , sinusoids. RMS is used in various fields, including electrical engineering. It can be calculated for a series of discrete values or for a continuously varying function.
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Niederreiter cryptosystem
In cryptography, the Niederreiter cryptosystem is a variation of the McEliece Cryptosystem developed in 1986 by Harald Niederreiter . It applies the same idea to the parity check matrix H of a linear code. Niederreiter is equivalent to McEliece from a security point of view. It uses a syndrome as ciphertext and the message is an error pattern. The encryption of Niederreiter is about ten times faster than the encryption of McEliece.
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Digital signal
A digital signal is a physical signal that is a representation of a sequence of discrete values, for example of an arbitrary bit stream, or of a digitized analog signal. The term digital signal can refer to a continuous-time waveform signal used in any form of digital communication.
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Algorithm
In mathematics and computer science, an algorithm Listen/ˈælɡərɪðəm/ (originating from al-Khwārizmī, the famous mathematician Muḥammad ibn Mūsā al-Khwārizmī) is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning. More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function.
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Computer program
A computer program (also software, or just a program) is a sequence of instructions written to perform a specified task with a computer. A computer requires programs to function, typically executing the program's instructions in a central processor. The program has an executable form that the computer can use directly to execute the instructions.
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