Projective system of a linear code

Let $C \leq 𝕂 𝑛 𝑞$ be a linear code, and $𝑐 𝑖 : C \to 𝕂 𝑞$ denote the $𝑖$ th coördinate function, and let $[𝑐 𝑖]$ denote the corresponding point in the projectivization $P (C *) ≅ P G (𝑘 - 1, 𝑞)$ . The multiset $𝔓 (C) = M ([𝑐 𝑖]) 𝑛 𝑖 = 1 \subseteq P (C *)$ is then called the projective system of $C$ . #m/def/code Iff all elements of $𝔓 (C)$ occur exactly once, then $C$ is a projective code.¹