Abstract
In this note we give a complete explicit factorization of\(x^{2^k }\) + 1 into irreducible polynomials overF p for a primep≡3 mod 4. As a result we can construct an irreducible polynomial overF p of degree of any power of 2. Some interesting properties of the coefficients of the irreducibles are noted. We also mention that our results may be useful in applying the Fast Fourier Transform over finite fields.
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Blake, I.F., Gao, S. & Mullin, R.C. Explicit factorization of\(x^{2^k }\) + 1 overF p with primep≡3 mod 4. AAECC 4, 89–94 (1993). https://doi.org/10.1007/BF01386832
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DOI: https://doi.org/10.1007/BF01386832