Irreducible polynomials and linear recurring arrays

Mulan Liu; Gary L. Mullen

doi:10.1016/s0166-218x(96)00112-6

Irreducible polynomials and linear recurring arrays

Mulan Liu
, Gary L. Mullen

Mathematics

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

Abstract

For α ∈ F_q the finite field of order q and β ∈ F_q(α), let F_q(α, β) = F_q(γ). We obtain an explicit formula for the minimal polynomial h^γ(x) of γ in terms of the greatest common divisor of two polynomials which are closely related to the minimal polynomials f_α(x) of α and g_β(x) of β. We also give an application of this result to linear recurring arrays.

Original language	English (US)
Pages (from-to)	93-99
Number of pages	7
Journal	Discrete Applied Mathematics
Volume	74
Issue number	1
DOIs	https://doi.org/10.1016/s0166-218x(96)00112-6
State	Published - Apr 4 1997

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/s0166-218x(96)00112-6

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abstract = "For α ∈ Fq the finite field of order q and β ∈ Fq(α), let Fq(α, β) = Fq(γ). We obtain an explicit formula for the minimal polynomial hγ(x) of γ in terms of the greatest common divisor of two polynomials which are closely related to the minimal polynomials fα(x) of α and gβ(x) of β. We also give an application of this result to linear recurring arrays.",

author = "Mulan Liu and Mullen, \{Gary L.\}",

note = "Funding Information: * Corresponding author. E-mail: [email protected]. {\textquoteright} Research supported by NNSF of China and the K.C.Wong",

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AU - Mullen, Gary L.

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PY - 1997/4/4

Y1 - 1997/4/4

N2 - For α ∈ Fq the finite field of order q and β ∈ Fq(α), let Fq(α, β) = Fq(γ). We obtain an explicit formula for the minimal polynomial hγ(x) of γ in terms of the greatest common divisor of two polynomials which are closely related to the minimal polynomials fα(x) of α and gβ(x) of β. We also give an application of this result to linear recurring arrays.

AB - For α ∈ Fq the finite field of order q and β ∈ Fq(α), let Fq(α, β) = Fq(γ). We obtain an explicit formula for the minimal polynomial hγ(x) of γ in terms of the greatest common divisor of two polynomials which are closely related to the minimal polynomials fα(x) of α and gβ(x) of β. We also give an application of this result to linear recurring arrays.

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Irreducible polynomials and linear recurring arrays

Abstract

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