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СЕМИНАРЫ |
2024-арные квазигруппы и смежные вопросы
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Координатная транзитивность расширенных совершенных кодов и их SQS И. Ю. Могильных, Ф. И. Соловьева |
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Аннотация: We continue the study a class of binary extended perfect propelinear Solov'eva codes constructed in the previous paper and consider their permutation automorphism (symmetry) groups and Steiner quadruple systems. We show that the automorphism group of the SQS of any such code coincides with the permutation automorphism group of the code. In particular, the isomorphism classes of these SQS's are complete invariants for the isomorphism classes of these codes. We obtain a criterion for the point transitivity of the automorphism group of SQS of proposed codes in terms of GL-equivalence (similar to EA-type equivalence for permutations of |