Swan-like results for binomials and trinomials over finite fields of odd characteristic

B. Hanson; D. Panario; D. Thomson

doi:10.1007/s10623-010-9476-7

Swan-like results for binomials and trinomials over finite fields of odd characteristic

B. Hanson, D. Panario, D. Thomson

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Swan (Pac. J. Math. 12:1099-1106, 1962) gives conditions under which the trinomial x ⁿ + x ^k + 1 over F₂ is reducible. Vishne (Finite Fields Appl. 3:370-377, 1997) extends this result to trinomials over extensions of F₂. In this work we determine the parity of the number of irreducible factors of all binomials and some trinomials over the finite field F_q, where q is a power of an odd prime.

Original language	English (US)
Pages (from-to)	273-283
Number of pages	11
Journal	Designs, Codes, and Cryptography
Volume	61
Issue number	3
DOIs	https://doi.org/10.1007/s10623-010-9476-7
State	Published - Dec 2011

All Science Journal Classification (ASJC) codes

Computer Science Applications
Applied Mathematics

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abstract = "Swan (Pac. J. Math. 12:1099-1106, 1962) gives conditions under which the trinomial x n + x k + 1 over F2 is reducible. Vishne (Finite Fields Appl. 3:370-377, 1997) extends this result to trinomials over extensions of F2. In this work we determine the parity of the number of irreducible factors of all binomials and some trinomials over the finite field Fq, where q is a power of an odd prime.",

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AU - Panario, D.

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AB - Swan (Pac. J. Math. 12:1099-1106, 1962) gives conditions under which the trinomial x n + x k + 1 over F2 is reducible. Vishne (Finite Fields Appl. 3:370-377, 1997) extends this result to trinomials over extensions of F2. In this work we determine the parity of the number of irreducible factors of all binomials and some trinomials over the finite field Fq, where q is a power of an odd prime.

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Swan-like results for binomials and trinomials over finite fields of odd characteristic

Abstract

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