Linear encoding of a group

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Definition

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

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