Irreducible polynomials over GF(2) with prescribed coefficients

Joseph L. Yucas, Gary L. Mullen

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For an even positive integer n, formulas were determined for the number of irreducible polynomials of degree n over GF(2) in which the coefficients of xn-1, xn-2 and xn-3 were specified in advance. GF(2)[x] was used to denote the ring of all polynomials with coefficients in GF(2). Formulas for the number of elements in GF(2n) with the first three traces specified were also given.

Original languageEnglish (US)
Pages (from-to)265-279
Number of pages15
JournalDiscrete Mathematics
Issue number1-3
Publication statusPublished - Jan 6 2004


All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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