Browsing by Subject "finite field"

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Open Access
Character sums, algebraic function fields, curves with many rational points and geometric Goppa codes
(1997) Özbudak, Ferruh
In this thesis we have found and studied fibre products of hyperelliptic and superelliptic curves with many rational points over finite fields. We have applied Goppa construction to these curves to get “good” linear codes. We have also found a nontrivial connection between configurations of affine lines in the affine plane over finite fields and fibre products of Rummer extensions giving “good” codes over F,2. Moreover we have calculated an important parameter of a class of towers of algebraic function fields over finite fields, which are studied recently.
Open Access
On lower degree bounds for vector invariants over finite fields
(2000) Madran, Uğur
The purpose of this thesis is to obtain a lower degree bound in modular invariant theory for a special case. More precisely, let G be any group and k be a finite field of positive characteristic p such that p divides |G| . We prove that if an invariant which has degree at most p —1 with respect to each variable can be written as a polynomial in orbit sums of monomials, then the invariant ring of m copies of the vector space V over k with dimV = n requires a generator of degree ^ ^ ^ provided that m > n where t and rii depends on the representation of G such that |'^'| < t < n + l and 2 < ni < p.