Minimum distance

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The term minimum distance is used in several ways:

In geometry, the minimum distance of a collection of points P in a space is the smallest distance between any two points of the space.

In coding theory, minimum distance is defined as the smallest distance between distinct codewords (often measured by Hamming distance). The minimum distance of a code gives a measure of how good it is at detecting and correcting errors, since a code with minimum distance $d$ can detect up to $d - 1$ errors or correct up to $\lfloor(d-1)/2 \rfloor$ errors in any codeword. Here the term minimum distance is typically used in reference to linear error-correcting codes.

1 Calculating minimum distance
- 1.1 Geometry
- 1.2 Coding Theory
2 References

[edit] Calculating minimum distance

[edit] Geometry

In the real plane, points P corresponding to all integer points (i, j) have a minimum distance of 1/2.
In two dimensional geometry, the minimum distance between two points can be found using the Pythagorean theorem.

[edit] Coding Theory

In coding theory minimum distance is often calculated using the Hamming distance of two codewords. It can also be calculated in other ways. For example, the minimum distance of a linear code can be calculated by finding the smallest number of linearly independent columns in its parity check matrix.