nLab
linear code

Contents

Idea

In coding theory, a linear code is an error correcting code which is linear, in that it is a linear subspace of a vector space over a finite field 𝔽 q\mathbb{F}_q. Specifically a binary linear code is a linear code over 𝔽 2\mathbb{F}_2.

A linear code is a linear subspace of a vector space of finite dimension dd over a prime field 𝔽 p\mathbb{F}_p, i.e. a vector space isomorphic to (𝔽 p) d(\mathbb{F}_p)^d, for some prime number pp (often p=2p = 2). The dimension dd of the vector space is also called the length of the linear code.

Examples

References

See also: