nLab
linear code

Contents

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

  • Patrick Morandi, Error Correcting Codes and Algebraic Curves , lecture notes New Mexico State University 2001. (pdf)

  • Jay A. Wood, Spinor groups and algebraic coding theory , J.Combinatorial Th. Series A 51 (1989) pp.277-313. (available online)

See also:

Last revised on May 5, 2021 at 02:46:00. See the history of this page for a list of all contributions to it.