@article{Danilović2024, 
author = {Doris Dumičić Danilović and Andrea Švob},
title = {On Hadamard  2- (51,25,12) and  2- (59,29,14) designs},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {8},
pages = {23047-23059},
keywords = {Hadamard 2-design, automorphism group, Frobenius group},
url = {https://www.sciopen.com/article/10.3934/math.20241120},
doi = {10.3934/math.20241120},
abstract = {In this paper, we classified Hadamard  2- (51,25,12) designs having a non-abelian automorphism group of order 10, i.e.,  Frob10≅Z5:Z2, where a subgroup isomorphic to  Z2 fixed setwise all the  Z5-orbits of the sets of points and blocks. Furthermore, we classified  2- (59,29,14) designs having a non-abelian automorphism group of order 14, i.e.,  Frob14≅Z7:Z2, where a subgroup isomorphic to  Z2 fixed setwise all the  Z7-orbits of the sets of points and blocks. We also showed that there was no Hadamard  2- (59,29,14) design with automorphism group  Frob21≅Z7:Z3, where a subgroup of order 3 fixed setwise all the  Z7-orbits of points and blocks. Additionally, we used Hadamard  2- (59,29,14) designs obtained to construct ternary linear codes and linear codes over the finite field of order 5. We constructed ternary self-dual codes and self-dual codes over the finite field of order 5 from the corresponding Hadamard matrices of order 60.}
}