Ternary codes from primitive representations of the group PSL2(9) and a new 2-(15,7,36) design

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Authors

  • Mohammad Reza Darafsheh
     School of Mathematics, Statistics, and Computer Science, College of Science, University of Tehran, Tehran ,IR
  • Reza Kahkeshani
     Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, ,IR

DOI:

https://doi.org/10.18311/jims/2022/23538

Keywords:

Design, Code, Automorphism group, Projective special linear group, Primitive permutation representation
05B05, 94B05, 20D45, 05E15, 05E20

Abstract

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.

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Published

2022-01-27

How to Cite

Darafsheh, M. R., & Kahkeshani, R. (2022). Ternary codes from primitive representations of the group <i>PSL<sub>2</sub>(9)</i> and a new 2-(15,7,36) design. The Journal of the Indian Mathematical Society, 89(1-2), 19–31. https://doi.org/10.18311/jims/2022/23538

Issue

Volume 89, Issue 1-2, January-June 2022

Section

Articles

License

Copyright (c) 2022 Mohammad Reza Darafsheh, Reza Kahkeshani

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2019-04-08
Accepted 2021-10-21
Published 2022-01-27

 

References

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