Irreducible cyclic groups over finite fields
Finding irreducible polynomials over finite fields
... fouiid in polvnomiil linic b^ niivc snrdi Ί(ιρ (ΐ\ is n«w ( tsil) si cn to bi rompiitiblc in.. pol>iH)iiuil tmR llif[r] ...
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Efficient Indexing of Necklaces and Irreducible Polynomials over Finite Fields
... n over alphabet Σ. A read-once branching program of length n over alphabet Σ is an acyclic directed graph with vertex layers numbered from 0 to n, where (1) layer 0 has a single start node, (2) there is a ...
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On the cohomology of finite groups over modular fields
... way to study the cohomology of a finite group, at least.. from an algebraic point of view, is within the.[r] ...
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Recent progress on weight distributions of cyclic codes over finite fields
... Abstract: Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding ...a cyclic code to estimate the ...
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In this paper we determine automorphism groups of cyclic alge- braic curves defined over finite fields of any characteristic
... an irreducible algebraic curve defined over ...automorphism groups of X g is very old problem in ...such groups, determining the equation of the curve when the group is given, determining the ...
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Irreducible representations of some finite groups and galois stability of integral representations
... representations over fields K and some related representations over Dedekind rings S in K is interesting to be ...of groups and orders in [1] and some other ...
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On group automata over finite fields
... algebras over finite fields is important for the representation theory (see ...abelian groups, gives a complete description of the Jacobson radicals of incidence rings of finite group automata over ...
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Factoring polynomials over finite fields
... The multiplicative group K ∗ is cyclic. More generally, any finite subgroup in the multiplicative group of a field is cyclic. A primitive element of K is by definition a generator of the group K ∗ . ...
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DAVENPORT PAIRS OVER FINITE FIELDS
... monodromy groups associated with the map f, or pairs of maps (f, g), extends considerably to include maps between algebraic curves defined over F q , and even to finite maps between higher- dimensional ...
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Galois Groups of Polynomials and the Construction of Finite Fields
... the irreducible ones, we can see clearly that, those without a constant term are ...the irreducible ones among the rest, we take each in turn and substitute all the elements of the field for , if none of ...
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Irreducible binary cubics and the generalised superelliptic equation over number fields
... • some prime ideal ω of the number field Q f generated by the Hecke eigenvalues of f, such that ω | l and ρ E,l ∼ = ρ f,ω . As we discussed in the previous section, since N l divides the conductor N of the elliptic curve ...
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On Skew Cyclic Codes over a Finite Ring
... Recently, there has been a vast interests on the study of cyclic codes. It is mainly due to their applications in power management [21], secret sharing [24, 23], steganography [14], etc. Also, these codes are easy ...
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Primitive irreducible linear groups
... Primitive Irreducible Linear Groups, In this chapter, we examine Pitting subgroups in primitive irreducible linear ...group over an algebraically closed field, it is known (see Suprunenko ...
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Factoring Polynomials Over Finite Fields: A Survey
... monic irreducible polyno- mials and e 1 , ...polynomial over a finite field is of interest not only inde- pendently but also for many applications in computer algebra, algebraic coding theory, ...
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Factoring Multivariate Polynomials over Finite Fields
... for irreducible components and their corresponding fields go through with minor modifications when we are working with reducible algebraic sets and their corresponding ...only over prime ...
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Integer Sequences and Matrices Over Finite Fields
... We can generalize the first part of Lemma 3 to allow for conjugacy class data in which the allowed partitions vary with the polynomials. The proof follows immediately from Lemma 1. Lemma 5 For each monic, ...
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Factorization Algorithms for Polynomials over Finite Fields
... polynomial over a field can be expressed as a product of ir- reducible ...of irreducible factors of a polynomial of positive ...polynomials over finite fields has great importance in coding ...mials ...
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Factoring Dickson polynomials over finite fields
... are irreducible over F q ; hence the stated factorization is ...a) over F q ...distinct irreducible polynomials in F q [X], which occur in cliques corresponding to the divisors d of ...) ...
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On linear algebraic groups over pseudoglobal fields
... algebraic groups over an algebraic function field K in one variable with a pseudofinite [5] constant field ...absolutely irreducible affine variety defined over k has a k-rational ...
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Finite irreducible linear 2-groups of degree 4
... distinct groups, all in the third line (and with = 0), precisely one with the three parameters in increasing ...six groups depend on the parameter values of G , since it follows from what has been said so ...
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