Existence and Cardinality of k-Normal Elements in Finite Fields

Normal bases and primitive elements over finite fields

Let q be a prime power, m ≥ 2 an integer and A = ( a b c d ) ∈ GL2(Fq), where A 6= ( 1 1 0 1 ) if q = 2 and m is odd. We prove an extension of the primitive normal basis theorem and its strong version. Namely, we show that, except for an explicit small list of genuine exceptions, for every q, m and A, there exists some primitive x ∈ Fqm such that both x and (ax+b)/(cx+d) produce a normal basis ...

THE CARDINALITY OF SETS OF k-INDEPENDENT VECTORS OVER FINITE FIELDS By S.B. Damelin

A set of vectors is k-independent if all its subsets with no more than k elements are linearly independent. We obtain a result concerning the maximal possible cardinality Indq(n, k) of a k-independent set of vectors in the n-dimensional vector space Fn q over the finite field Fq of order q. Namely, we give a necessary and sufficient condition for Indq(n, k) = n + 1.

On the existence of some specific elements in finite fields of characteristic 2

Article history: Received 31 August 2011 Revised 12 April 2012 Accepted 16 April 2012 Available online 21 April 2012 Communicated by D. Panario

On Completely Free Elements in Finite Fields

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...