Projective code

A $[𝑘, 𝑛] -$ linear code $C \leq 𝕂 𝑛 𝑞$ is said to be projective iff it meets the following equivalent conditions:¹² #m/def/code

its Orthogonal code $C ⟂$ has minimum distance $𝑑 \geq 3$ ;
any generator matrix $𝐺$ of $C$ has pairwise linearly independent columns; or
every point in the projective system $𝔓 (C)$ occurs exactly once.

#state/tidy | #lang/en | #SemBr

1999. Introduction to coding theory, §3.3, p. 38 ↩
2017. The graphs of projective codes, §2.2, p. 3 ↩