Abstract
In this paper we present a method to computeall the irreducible and primitive polynomials of degreem over the finite fieldGF(q). Our method finds each new irreducible or primitive polynomial with a complexity ofO(m) arithmetic operations inGF(q). The best previously known methods [3], [10] use the Berlekamp-Massey algorithm [7] and they have a complexityO(m 2). We reach mis improvement taking into account a systolic implementation [2] of the extended Euclidean algorithm instead of using the Berlekamp-Massey algorithm.
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This work was supported in part by Spanish Grant CICYT TIC91-0472.
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Rifà, J., Borrell, J. A fast algorithm to compute irreducible and primitive polynomials in finite fields. Math. Systems Theory 28, 13–20 (1995). https://doi.org/10.1007/BF01294593
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DOI: https://doi.org/10.1007/BF01294593