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On the parameters of extended primitive cyclic codes and the related designs
Haode Yan, Yanan Yin · 2023-06-13 · via cs.IT updates on arXiv.org

Very recently, Heng et al. studied a family of extended primitive cyclic codes. It was shown that the supports of all codewords with any fixed nonzero Hamming weight of this code supporting 2-designs. In this paper, we study this family of extended primitive cyclic codes in more details. The weight distribution is determined. The parameters of the related $2$-designs are also given. Moreover, we prove that the codewords with minimum Hamming weight supporting 3-designs, which gives an affirmative solution to Heng's conjecture.

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