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For a fixed length n, the Hamming distance is a metric on the set of the words of length n (also known as a Hamming space), as it fulfills the conditions of non-negativity, symmetry, the Hamming distance of two words is 0 if and only if the two words are identical, and it satisfies the triangle inequality as well: [2] Indeed, if we fix three words a, b and c, then whenever there is a ...
In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics.
For each integer r ≥ 2 there is a code-word with block length n = 2 r − 1 and message length k = 2 r − r − 1. Hence the rate of Hamming codes is R = k / n = 1 − r / (2 r − 1) , which is the highest possible for codes with minimum distance of three (i.e., the minimal number of bit changes needed to go from any code word to any other ...
The two squared formulas inside the square root give the areas of squares on the horizontal and vertical sides, and the outer square root converts the area of the square on the hypotenuse into the length of the hypotenuse. [3] It is also possible to compute the distance for points given by polar coordinates.
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
The above formula for the maximum overhang of blocks, each with length and mass , stacked one at a level, can be proven by induction by considering the torques on the blocks about the edge of the table they overhang. The blocks can be modelled as point-masses located at the center of each block, assuming uniform mass-density.
The advantage of choosing a primitive polynomial as the generator for a CRC code is that the resulting code has maximal total block length in the sense that all 1-bit errors within that block length have different remainders (also called syndromes) and therefore, since the remainder is a linear function of the block, the code can detect all 2 ...
The total length of the rope L can be written as = + +, where K is the constant length of rope that passes over the pulleys and does not change as the block and tackle moves. The velocities V A and V B of the points A and B are related by the constant length of the rope, that is