Subspace coverings and generalized covering radii of generalized Zetterberg codes

@misc{li2026subspace,
  title = {{Subspace coverings and generalized covering radii of generalized Zetterberg codes}},
  author = {Shitao Li and Yang Li and Gaojun Luo and Zhonghua Sun},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25115},
  eprint = {2609.25115},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25115},
}

TY  - UNPB
TI  - Subspace coverings and generalized covering radii of generalized Zetterberg codes
AU  - Shitao Li
AU  - Yang Li
AU  - Gaojun Luo
AU  - Zhonghua Sun
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.25115
UR  - https://arxiv.org/abs/2609.25115
AB  - Generalized covering radii measure how many columns of a parity-check matrix are needed to generate several syndromes simultaneously. Their finite-geometric counterparts are (ρ,t)-saturating sets, for which every t-dimensional subspace is contained in a subspace generated by at most ρ prescribed vectors. We investigate this covering problem for the norm-one configurations associated with generalized Zetterberg codes. We establish the upper bound 2t+1 over every nonbinary finite field and in an explicit binary range, together with complementary lower bounds obtained by counting subspaces and constructing subfield obstructions. For an explicit range of large t, these configurations are t-strong blocking sets, and the t^th generalized covering radius attains its minimum possible value t. For binary Zetterberg codes, we determine the second generalized covering radius in every extension degree and prove that the third radius is seven for an infinite subfamily.
ER  -