Abstract
In this paper, we present a method to compute all the irreducible and primitive polynomials of degree m over a finite field. We also describe two concrete implementations of our method with respective time complexities O(m 2 + m log m) and O(m 2 + log m). These implementations, using in parallel different devices introduced to operate in these fields [1], [7], allows us to reduce the time complexity of our method below that of the best previously known methods [3]. Our algorithm is especially well-suited for applications using large finite fields.
This work was supported in part by Spanish DGICYT/UAB Grant N. 113118
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Rifà, J., Borrell, J. (1991). Improving the time complexity of the computation of irreducible and primitive polynomials in finite fields. In: Mattson, H.F., Mora, T., Rao, T.R.N. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1991. Lecture Notes in Computer Science, vol 539. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54522-0_123
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DOI: https://doi.org/10.1007/3-540-54522-0_123
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