Recursive constructions of k-normal polynomials over finite fields

2016/10/15 by Alizadeh, Mahmood, Mehrabi, Saeid
#Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1610.05684

Abstract

The paper is devoted to produce infinite sequences of k-normal polynomials F_u(x)∈ \mathbbF_q[x] of degrees np^u ~ (u≥ 0), for a suitably chosen initial k-normal polynomial F₀(x)∈ \mathbbF_q[x] of degree n over \mathbbF_q by iteratively applying the transformation x→ (x^p-x)/(x^p-x+δ), where δ∈ \mathbbF_q and 0≤ k≤ n-1.

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