The term minimum distance is used in several ways:

• In geometry
  Geometry
  Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
  
  , 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
  Coding theory
  Coding theory is the study of the properties of codes and their fitness for a specific application. Codes are used for data compression, cryptography, error-correction and more recently also for network coding...
  
  , the term refers to the minimum distance of a block code.

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
  Pythagorean theorem
  In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle...
  
  .

Coding Theory

In coding theory minimum distance is often calculated using the Hamming distance

Hamming distance

In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different...

 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.