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Original scientific paper

Designs and binary codes from maximal subgroups and conjugacy classes of M11

Gareth Amery ; School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, South Africa
Stuart Gomani ; School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, South Africa
Bernardo Gabriel Rodrigues ; Department of Mathematics and Applied Mathematics, University of Pretoria, South Africa


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Abstract

By using a method of construction of block-primitive and point-transitive 1-designs, in this paper we determine all block-primitive and point-transitive 1-(v,k,λ)-designs from the maximal subgroups and the conjugacy classes of elements of the small Mathieu group M11. We examine the properties of the 1-(v,k,λ)-designs and construct the codes defined by the binary row span of their incidence matrices. Furthermore, we present a number of interesting Δ-divisible binary codes invariant under M11.

Keywords

primitive designs, linear code, Mathieu group M11

Hrčak ID:

261511

URI

https://hrcak.srce.hr/261511

Publication date:

26.8.2021.

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