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Kahkeshani, Reza
- Ternary codes from primitive representations of the group PSL2(9) and a new 2-(15,7,36) design
Authors
1 School of Mathematics, Statistics, and Computer Science, College of Science, University of Tehran, IR
2 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, IR
Source
The Journal of the Indian Mathematical Society, Vol 89, No 1-2 (2022), Pagination: 19–31Abstract
In this paper, we construct, using computations withMagma, a ternary code C from a primitive permutation representation of degree 15 of the group PSL2(9) by Key-Moori Method 1. The code C is an optimal code invariant under the group S6. We consider the action of the automorphism group S6 on C and its dual. By taking the support of any codeword ? of weight l and orbiting it under S6, 1-(15, l, kl) designs are obtained, where kl = l|?S6 |/15. For any codeword, the structure of the stabilizer in S6 is determined and primitivity of S6 on each design is examined. It is shown that the complement of one of these designs is actually a new design D with parameters 2-(15, 7, 36). Moreover, Aut(D) ? S6.
Keywords
Design, Code, Automorphism Group, Projective Special Linear Group, Primitive Permutation Representation.References
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