engleski

Finding unitals in symmetric designs using a modified genetic algorithm

We present an algorithm for finding unitals as subdesigns of symmetric designs. Further, we employ this algorithm to find unitals in symmetric (66, 26, 10) designs. This problem is here formulated as a combinatorial optimization problem whose solutions are binary matrices. Using the modified genetic algorithm (MGA) we have found eleven new 2-(11, 5, 10) designs (unitals) in the symmetric (66, 26, 10) design admitting an automorphism of order 55. In addition, we have found 63 new unitals in the symmetric (36, 15, 6) design with the full automorphism group of order 42.

symmetric design ; unital ; genetic algorithm

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