[[Code]]
# Systematic code

A $q$-ary [[code]] $\mathcal{C}$ is said to be **systematic** on positions $\{ r_{i} \}_{i=1}^k$ iff a given codeword $c \in \mathcal{C}$ is completely determined by the values of $c_{r_{i}}$, #m/def/code 
i.e. $\abs{\mathcal{C}} = q^k$ 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.[^1999]

  [^1999]: 1999\. [[Sources/@vanlintIntroductionCodingTheory1999|Introduction to coding theory]], §3.2, p. 36


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