Abstract
Existing bounds on the minimum weight d ⊥ of the dual 7-ary code of a projective plane of order 49 show that this must be in the range 76 ≤ d ⊥ ≤ 98. We use combinatorial arguments to improve this range to 88 ≤ d ⊥ ≤ 98, noting that the upper bound can be taken to be 91 if the plane has a Baer subplane, as in the desarguesian case. A brief survey of known results for the minimum weight of the dual codes of finite projective planes is also included.
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Dedicated to Dan Hughes on the occasion of his 80th birthday.
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Key, J.D., Ngwane, F.F. A lower bound for the minimum weight of the dual 7-ary code of a projective plane of order 49. Des. Codes Cryptogr. 44, 133–142 (2007). https://doi.org/10.1007/s10623-007-9072-7
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DOI: https://doi.org/10.1007/s10623-007-9072-7