Abstract
It is known that any square matrix A of size n over a field of prime characteristic p that has rank less than n/(p − 1) has a permanent that is zero. We give a new proof involving the invariant X p . There are always matrices of any larger rank with non-zero permanents. It is shown that when the rank of A is exactly n/(p − 1), its permanent may be factorized into two functions involving X p .
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Communicated by J. W. P. Hirschfeld.
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Glynn, D.G. The factorization of the permanent of a matrix with minimal rank in prime characteristic. Des. Codes Cryptogr. 62, 175–177 (2012). https://doi.org/10.1007/s10623-011-9501-5
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DOI: https://doi.org/10.1007/s10623-011-9501-5