Binary linear codes with a fixed point free permutation automorphism of order three
<|reference_start|>Binary linear codes with a fixed point free permutation automorphism of order three: We investigate the structural properties of binary linear codes whose permutation automorphism group has a fixed point free automorphism of order $3$. We prove that up to dimension or codimension $4$, there is no binary linear code whose permutation automorphism group is generated by a fixed point free permutation of order $3$. We also prove that there is no binary $5$-dimensional linear code whose length is at least $30$ and whose permutation automorphism group is generated by a fixed point free permutation of order $3$.<|reference_end|>
@article{aksu2024binary,
    title={Binary linear codes with a fixed point free permutation automorphism of
  order three},
    author={Fatma Altunbulak Aksu, Roghayeh Hafezieh and .Ipek Tuvay},
    journal={arXiv preprint arXiv:2402.10667},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.10667},
    primaryClass={cs.IT math.IT}
}