Abstract
In a 2013 article, Ball and Blokhuis proved a congruence for a linear \([n,k]\) code with a codeword of weight \(n\). Their proof is based on a character sum on the group of \(1\times (k-1)\) nonzero matrices. We show that the same argument works for groups of \(r\times (k-1)\) matrices for every \(r, 1\le r \le k\). So we extend their theorem by giving a family of \(k\) congruences.
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Acknowledgments
The author would like to thank Simeon Ball for his helpful answers to questions posed. The author also thanks the reviewers of the manuscript for their insightful comments
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Communicated by S. Ball.
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Özen, İ. Generalized weights and the Ball–Blokhuis congruence. Des. Codes Cryptogr. 79, 231–235 (2016). https://doi.org/10.1007/s10623-015-0046-x
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DOI: https://doi.org/10.1007/s10623-015-0046-x