By B. Loewe (ed.)

This quantity is either a tribute to Ulrich Felgner's examine in algebra, common sense, and set idea and a powerful learn contribution to those components. Felgner's former scholars, pals and collaborators have contributed 16 papers to this quantity that spotlight the cohesion of those 3 fields within the spirit of Ulrich Felgner's personal learn. The reader will locate first-class unique learn surveys and papers that span the sector from set concept with no the axiom of selection through model-theoretic algebra to the maths of intonation.

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V) g23 ist perfekt. (vi) g24 hat die erzeugende Funktion A(Z) = 1 + 759· Z8 + 2576. Z12 + 759. h. es gibt je 759 W6rter mit Hamming-Norm 8 bzw. 16 und 2576 W6rter mit Hamming-Norm 12. Beweis. (i) Jedes Codewort aus 1{ n 1{* hat die folgende Gestalt, man benutze die Erzeugermatrizen von oben, (a, b, c, d, a + b + c, a + c + d, b + c + d, a + b + d) (b' = + c' + d', a' + c' + d', a' + b' + c' , a' , b' , c' , d' ,a' + b' + d' ) Daraus folgt a = b' + c' + d' = c c = a' + b' + c' = b ::::} a = b = c b = a' + c' + d' = a + b + d ::::} a = d .

G(x) n ( . ) : A x A ~ lF2 , (1, g) := xEV 34 1. Lineare Codes Wir setzen: M:={l, ... ,m} IC := M - I fur I c M supp(x):= {i EM; Xi f:. O} fur X = (Xl, ... ,Xn) E V = IF;' Zi i-te Koordinatenfunktion hs := I1iEI(Zi + Si + 1) fUr Ie M , S E V JI:= ho SI := supp(JI) := {x E V; JI(x) = I} Man rechnet einige einfache Eigenschaften leicht nach: 1. hs(x) = 1 {:=} Xi = Si fUr alle i E I . X E SI {:=} JI(x) = 1 {:=} Xi = 0 fUr alle i E I . 2. SI ist ein Untervektorraum von V und es gilt V = SI EB SIc. 3.

Iii) Es ist lFqm /lFq eine galoissche Erweiterung mit zyklischer Galoisgruppe. Der Probeniusautomorphismus € ~ €q ist ein kanonisches erzeugendes Element der Galoisgruppe. Zum Beispiel gilt im Fall q Es sei nun = 2 fiir die Beziehung zwischen n 3 5 7 9 11 13 m 2 4 3 6 10 12 Xn - 1 = n und m: h(X)· ... · h(X) die Zerlegung in irreduzible Faktoren iiber lFq . 1st as Nullstelle von fi(X) , so auch aIle Konjugierten 2 as, (as)q, (as)q , von as. Man teilt nun diese in Aquivalenzklassen bzgl. der Operation des Frobenius ein.

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