# Linear encoding of a group

From Groupprops

## Definition

A **linear encoding of a group** is the following data:

- An integer , a field and the standard encoding for (as described in encoding of symmetric groups)
- A specification of the given group as a subgroup of the general linear group by means of a generating set (preferably a small one)
- A membership test for as a subgroup of the general linear group

A linear encoding can also be viewed as a concrete, or explicit, description using a failthful linear representation.

## Related notions

Permutation encoding is the notion for encoding as a subgroup of a symmetric group.