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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

Sažetak

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 \({\rm M}_{11}\).

Ključne riječi

primitive designs, linear code, Mathieu group \({\rm M}_{11}\)

Hrčak ID:

261511

URI

https://hrcak.srce.hr/261511

Datum izdavanja:

26.8.2021.

Posjeta: 865 *