Linear code

Projective code

A [𝑘,𝑛] −linear code C ≤𝕂𝑛𝑞 is said to be projective iff it meets the following equivalent conditions:¹² code

• its Orthogonal code C⟂ has ^minimumDistance 𝑑 ≥3;

• any ^generator 𝐺 of C has pairwise linearly independent columns; or

• every point in the projective system 𝔓(C) occurs exactly once.

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Footnotes

1. 1999. Introduction to coding theory, §3.3, p. 38 ↩

2. 2017. The graphs of projective codes, §2.2, p. 3 ↩