Covering radius of generalized Zetterberg codes of even characteristic

Official URL: https://dx.doi.org/10.1109/TIT.2026.3697587

For integers u ≥ 2 and s ≥ 1, let q0 = 2u, and let Cs(q0) be the generalized Zetterberg code of length n = qs0 + 1 over the finite field Fq0 of characteristic 2. For odd characteristic, the covering radius of Cs(q0) was determined recently, whereas the case of even characteristic remained open. In this paper, we determine the covering radius of generalized Zetterberg codes over finite fields of characteristic 2, thereby solving this open problem. Our approach uses methods from the theory of algebraic curves over finite fields. As an application, we obtain an infinite family of quasi-perfect codes.