New algorithms enhance computations of permutation polynomials in finite fields, suggesting improved bounds for Hamming distances.
We develop algorithms for computing permutation polynomials (PPs) using normalization, so-called F-maps and G-maps, and the Hermite criterion. This allows for a more efficient computation of PPs for larger degrees and for larger finite fields. We use this to improve some lower bounds for M(n,D), the maximum number of permutations on n symbols with a pairwise Hamming distance of D.
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Bereg et al. (2025) studied this question.
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