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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Дискретная математика и математическая кибернетика
Coordinate transitivity of a class of extended perfect codes and their SQS
I. Yu. Mogilnykhabc, F. I. Solov'evacb a Tomsk State University, Regional Scientific and Educational Mathematical Center, 36, Lenin ave., Tomsk, 634050, Russia
b Sobolev Institute of Mathematics, 4, Acad. Koptyuga ave., Novosibirsk, 630090, Russia
c Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
Аннотация:
We continue the study of the class of binary extended perfect propelinear 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 $\mathrm{GL}$-equivalence (similar to EA-type equivalence for permutations of $F^r$). Based on these results we suggest a new construction for coordinate transitive and neighbor transitive extended perfect codes.
Ключевые слова:
extended perfect code, concatenation construction, transitive code, neighbor transitive code, transitive action, regular subgroup, isomorphism problem, transitive Steiner quadruple system, coordinate transitive code.
Поступила 30 марта 2020 г., опубликована 14 сентября 2020 г.
Образец цитирования:
I. Yu. Mogilnykh, F. I. Solov'eva, “Coordinate transitivity of a class of extended perfect codes and their SQS”, Сиб. электрон. матем. изв., 17 (2020), 1451–1462
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/semr1295 https://www.mathnet.ru/rus/semr/v17/p1451
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