finite fieldGiven an integer n > 1, for which prime powers q does everytranslate {θ + a : a ∈ F_q} (with F_q(θ)=F_(q~n) ) contain a primitive element of Further, for which prime powers does every line {a(θ + a) : a∈ F_q}(with F_q(θ) = F_(q~n) and a ...
ToFiniteField, FromFiniteField — convert expressions to and from finite field versions FiniteFieldIndex, FromFiniteFieldIndex — convert to and from the index representation FiniteFieldElementTrace ▪ FiniteFieldElementNorm ▪ MinimalPolynomial ▪ MultiplicativeOrder ▪ FiniteFieldElementPrimitiveQ Pol...
FiniteFieldElement[ff, ind] 给出索引为 ind 的有限域 ff 的元素. FiniteFieldElement[ff, {c0, c1, c2, ...}] 给出有限域 ff 的元素 c0 + c1 \[Theta] + c2 \[Theta]^2 + ...,其中 \[Theta] 是 ff 的域生成器.
On the product of two primitive elements of maximal subfields of a finite field Finite Fields and Their ApplicationsPetrenko B.V.: On the product of two primitive elements of maximal subfields of a finite field. J. Pure Appl. ... BV Petrenko - 《Finite Fields & Their Applications》 被引...
- ``x`` - gap finite field element - ``F`` - Sage finite field OUTPUT: element of F EXAMPLES:: sage: x = gap('Z(13)') sage: F = GF(13, 'a') sage: F(x) 2 sage: F(gap('0*Z(13)')) 0 sage: F = GF(13^2, 'a') ...
Define Finite extension. Finite extension synonyms, Finite extension pronunciation, Finite extension translation, English dictionary definition of Finite extension.
(Such a polynomial is guaranteed to exist, once we know that a finite field of size q exists: just take the minimal polynomial of any primitive element for that field over the subfield Fp.) Then Fp[T]/(f(T)) is a field of size q. Here, Fp[T] denotes the ring of all ...
By definition primitive and 2 2 -primitive elements of a finite field extension \mathbb{F}_{q^n} \mathbb{F}_{q^n} have order q^n-1 q^n-1 and (q^n-1)/2 (q^n-1)/2 , respectively. We have already shown that, with minor reservations, there exists a primitive element and a ...
When this form is used, the package automatically selects an irreducible polynomial, with coefficients given by ilist and with the property that GF[p,ilist][{0,1}] is a primitive element of the field. It is possible to provide your own irreducible polynomial by giving it explicitly, as in...
IntroductionLetτη,ηbepositiveintegers,q=pmapowerofa primenumberp,IFgafinitefieldofqelements,andIF^afiniteextensionofJFqofdegreen.Itiswellknown(see[1],[2])thateachfieldIF^nhasanormalbasisoverIF^,i.e.abasisoftheformn-la, a,...,agFurther,IFgnhasa primitiveelementϋwhosepowersΰ, ΰ2,....