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In the thesis solutions of problems from finite geometries related to problems from coding theory are presented. The text is structured in 5 chapters. Chapter 1 is introductory. Chapter 2 contains definitions and results on pointsets in geometries and codes over finite fields. In Chapter 3 the maximal deviation tq(k) of a linear [n,k,d]q-code from the Griesmer bound is investigated. It is proved that for even dimensions it holds tq(k) ≤qk/2. For the case of q even the hypoyhesis of Ball is proved, namely tq(3)<logq. For q perfect square the inequality tq(k)≤qk/2-1 is proved. The nonexistence of some hypothetical arcs in PG(4,4) is proved. Thus ten open cases for n4(5,d) are solved. In Chapter 4 (t mod q)-arcs are introduced. It is proved that the extendability of a t-quasidivisible arc is equivalent to the existence of a hyperplane in the support of special dual arc which is a (t mod q)-arc. It is proved that every (t mod p)-arc, p– a prime, is a sum of complements of hyperplanes. In particular, every (t mod p)-arc is a sum of lifted arcs. In the case of plane arcs, it is proved that every (t mod p)-arc is a sum of at most p lifted arcs. One of the four open cases for n5(4,d) is solved. A new general construction for affine blocking sets is described. As a special case a new infinite class of t-blocking sets with t=q-n+2 meeting the Bruen bound is constructed. This class gives rise to an infinite family of optimal affine blocking sets meeting the Ball bound from 2000.
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