Constructing transitive permutation groups

Constructing transitive permutation groups

This paper presents a new algorithm to classify all transitive subgroups of the symmetric group up to conjugacy. It has been used to determine the transitive groups of degree up to 30.

Constructing error-correcting binary codes using transitive permutation groups

Let A2(n, d) be the maximum size of a binary code of length n and minimum distance d. In this paper we present the following new lower bounds: A2(18, 4) ≥ 5632, A2(21, 4) ≥ 40960, A2(22, 4) ≥ 81920, A2(23, 4) ≥ 163840, A2(24, 4) ≥ 327680, A2(24, 10) ≥ 136, and A2(25, 6) ≥ 17920. The new lower bounds are a result of a systematic computer search over transitive permutation groups.

On Transitive Permutation Groups

We assign names and new generators to the transitive groups of degree up to 15, reflecting their structure.

Generating Transitive Permutation Groups

Abstract Groups as Doubly Transitive Permutation Groups *

Groups as Doubly Transitive Permutation Groups *