Minimum distance

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, the term refers to the minimum distance of a block code.

Calculation

Geometry

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

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 dependent columns in its parity check matrix.

See also

• Dijkstra's algorithm

References

• Hill, Raymond. (1988). A First Course In Coding Theory, New York: Oxford University Press.