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In computing, a linear-feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state. The most commonly used linear function of single bits is exclusive-or (XOR). Thus, an LFSR is most often a shift register whose input bit is driven by the XOR of some bits of the overall shift register value.
In their paper, [1] Meier and Steffelbach prove that a LFSR-based self-shrinking generator with a connection polynomial of length L results in an output sequence period of at least 2 L/2, and a linear complexity of at least 2 L/2-1. Furthermore, they show that any self-shrinking generator can be represented as a shrinking-generator.
In fact, every linear-feedback shift register with maximum cycle length (which is 2 n − 1, where n is the length of the linear-feedback shift register) may be built from a primitive polynomial. [2] In general, for a primitive polynomial of degree m over GF(2), this process will generate 2 m − 1 pseudo-random bits before repeating the same ...
The Berlekamp–Massey algorithm is an algorithm that will find the shortest linear-feedback shift register (LFSR) for a given binary output sequence. The algorithm will also find the minimal polynomial of a linearly recurrent sequence in an arbitrary field .
Zoom lenses are often described by the ratio of their longest to shortest focal lengths. For example, a zoom lens with focal lengths ranging from 100 mm to 400 mm may be described as a 4:1 or "4×" zoom. Typical zoom lenses cover a 3.5× range, for example 24–90 mm (standard zoom) or 60–200 mm (telephoto zoom).
Lens mount Viewfinder coverage Metering zones Focus points Lowest ISO Highest ISO Cont. shtg LCD size Live view Movie mode Memory card Dimensions (mm) Weight (g) [1] Announced (date) Ref. Canon: 5D Mark IV: Full frame: 30.1 EF 100 252 61 50 102400 7 3.2 yes yes CF+SD: 150.7×116.4×75.9 890 Aug 2016: Canon: 1D X Mark II: Full frame: 20.2 EF ...
The significance of being a Galois extension is that the extension has a Galois group and obeys the fundamental theorem of Galois theory. [a] A result of Emil Artin allows one to construct Galois extensions as follows: If E is a given field, and G is a finite group of automorphisms of E with fixed field F, then E/F is a Galois extension. [2]
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