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Linear codes and a projective plane of order 10
Liška, Ondřej ; Drápal, Aleš (advisor) ; Vojtěchovský, Petr (referee)
Projective plane of order 10 does not exist. Proof of this assertion was finished in 1989 and is based on the nonexistence of a binary code C generated by the incidence vectors of the plane's lines. As part of the proof of the nonexistence of code C, the coefficients of its weight enumerator were studied. It was shown that coefficients A12, A15, A16 and A19 have to be equal to zero, which contradicted other findings about the relationship among the coefficients. Presented diploma thesis elaborately analyses the phases of the proof and, in several places, enhances them with new observations and simplifications. Part of the proof is generalized for projective planes of order 8m + 2. 1
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Linear codes and a projective plane of order 10
Liška, Ondřej ; Drápal, Aleš (advisor) ; Vojtěchovský, Petr (referee)
Projective plane of order 10 does not exist. Proof of this assertion was finished in 1989 and is based on the nonexistence of a binary code C generated by the incidence vectors of the plane's lines. As part of the proof of the nonexistence of code C, the coefficients of its weight enumerator were studied. It was shown that coefficients A12, A15, A16 and A19 have to be equal to zero, which contradicted other findings about the relationship among the coefficients. Presented diploma thesis elaborately analyses the phases of the proof and, in several places, enhances them with new observations and simplifications. Part of the proof is generalized for projective planes of order 8m + 2. 1
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Magic squares
SUCHÁ, Lucie
This diploma thesis deals with basic features of magic squares and analyses these features with regard to usability during the teaching at elementary schools. Magic squares are known for hundreds years and since then they have changed due to various modifications, from which other kinds were derived. The first part of the thesis is therefore dedicated to the history. Next chapter deals with the construction of magic squares. The following chapters study similar games as Sudoku, Kakuro and Latin squares. The final part of the thesis is dedicated to the usability of magic squares in teaching mathematics. To practice the given topic, the worksheets which are divided according to their difficulty, were created.
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