Systematic code

A $𝑞$ -ary code $C$ is said to be systematic on positions ${𝑟 𝑖} 𝑘 𝑖 = 1$ iff a given codeword $𝑐 \in C$ is completely determined by the values of $𝑐 𝑟 𝑖$ , code i.e. $| C | = 𝑞 𝑘$ and there is exactly one codeword for every choice of the coördinates in the positions. Such codes are sometimes called separable, since one may separate information digits from redundant (check) digits.¹