Coding theory | String metrics
In coding theory, the Lee distance is a distance between two strings and of equal length n over the q-ary alphabet {0, 1, âĻ, q â 1} of size q âĨ 2. It is a metric defined as If q = 2 or q = 3 the Lee distance coincides with the Hamming distance, because both distances are 0 for two single equal symbols and 1 for two single non-equal symbols. For q > 3 this is not the case anymore; the Lee distance between single letters can become bigger than 1. However, there exists a Gray isometry (weight-preserving bijection) between with the Lee weight and with the Hamming weight. Considering the alphabet as the additive group Zq, the Lee distance between two single letters and is the length of shortest path in the Cayley graph (which is circular since the group is cyclic) between them. More generally, the Lee distance between two strings of length n is the length of the shortest path between them in the Cayley graph of . This can also be thought of as the quotient metric resulting from reducing Zn with the Manhattan distance modulo the lattice qZn. The analogous quotient metric on a quotient of Zn modulo an arbitrary lattice is known as a Mannheim metric or Mannheim distance. The metric space induced by the Lee distance is a discrete analog of the elliptic space. (Wikipedia).
This video show how to use the distance formula to determine the distance between two points. It also shows how it is derived from the Pythagorean theorem. http://mathispower4u.yolasite.com/
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From playlist Geometry
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This video shows an example of determining the length of a segment on the coordinate plane by using the distance formula. Complete Video List: http://www.mathispower4u.yolasite.com or http://www.mathispower4u.wordpress.com
From playlist Using the Distance Formula / Midpoint Formula
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From playlist Find the Distance of the Line Segment
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From playlist Best Videos | Big Think
Applying the distance formula to find the distance between two points
đ Learn how to find the distance between two points. The distance between two points is the length of the line joining the two points in the coordinate plane. To find the distance between two points in the coordinate plane, we make use of the formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2). đ
From playlist Find the Distance of the Line Segment
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