The third generalized covering radius for binary primitive double-error-correcting BCH codes

Official URL: https://dx.doi.org/10.1016/j.ffa.2025.102749

We prove that the third generalized covering radius of binary primitive double-error-correcting BCH codes of length 2 m − 1 is 7 if m ≥ 8 is an even integer. We also prove that the third generalized covering radius of binary primitive double-error-correcting BCH codes of length 2 m − 1 is either 6 or 7 if m ≥ 9 is an odd integer. We use some methods derived from the theory of algebraic curves over finite fields in our proofs and we obtain some further related results.