Original scientific paper
Designs and binary codes from maximal subgroups and conjugacy classes of \({\rm M}_{11}\)
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
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-\((v, k, \lambda)\)-designs from the maximal subgroups and the conjugacy classes of elements of the small Mathieu group \({\rm M}_{11}\). We examine the properties of the 1-\((v, k, \lambda)\)-designs and construct the codes defined by the binary row span of their incidence matrices. Furthermore, we present a number of interesting \(\Delta\)-divisible binary codes invariant under \({\rm M}_{11}\).
Keywords
primitive designs, linear code, Mathieu group \({\rm M}_{11}\)
Hrčak ID:
261511
URI
Publication date:
26.8.2021.
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