[[Coding theory MOC]]
# Divisible code

A $q$-ary [[linear code]] $\mathcal{C} \leq \mathbb{K}_{q}^n$ is $m$-divisible iff all codewords have [[Hamming distance|Hamming weight]] divisible by $m$, #m/def/code 
i.e. $\wt \vab c \in m\mathbb{Z}$ for all $\vab c \in \mathcal{C}$.
In particular,

- a $2$-divisible code is called an **even code**;
- a $4$-divisible code is called a **doubly-even code**.

## Properties

- An even [[binary linear code]] is a linear subcode of _the_ [[even binary code]].

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