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 $\mathbb{F}_q$. Specifically a binary linear code is a linear code over $\mathbb{F}_2$.
A linear code is a linear subspace of a vector space of finite dimension $d$ over a prime field $\mathbb{F}_p$, i.e. a vector space isomorphic to $(\mathbb{F}_p)^d$, for some prime number $p$ (often $p = 2$). The dimension $d$ of the vector space is also called the length of the linear code.
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)
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