Binary BCH codes are shown whose minimum distance exceeds the Bose distance by 2^{floor((m-1)/3)-1}, a gap of order n^{1/3}, refuting Charpin's bounded-gap conjecture.
On the minimum distances of some families of BCH codes,
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Counterexamples to Charpin's Conjecture on BCH codes
Binary BCH codes are shown whose minimum distance exceeds the Bose distance by 2^{floor((m-1)/3)-1}, a gap of order n^{1/3}, refuting Charpin's bounded-gap conjecture.