# Binary linear code

From Groupprops

## Contents

## Definition

A **binary linear code** is a vector subspace of the power set of a finite set . Here, the power set of a finite set is treated as a vector space via the usual XOR operation.

## Value taken for terms from general theory of linear codes

### Message length

This is the dimension of the vector subspace.

### Code length

This is the size of the set .

### Weight of the code

This is simply the minimum cardinality among all members of (note that each member of is a subset of so it makes sense to talk of its cardinality).