扩展完美码及其SQS的坐标传递性
Coordinate transitivity of extended perfect codes and their SQS
摘要：
我们继续研究在前一篇文章中构造的二元扩展完美propelinear码类，并考虑它们的置换自同构（对称）群和Steiner四重系统。我们表明，自同构群的SQS的任何这样的代码符合置换自同构群的代码。特别地，这些代码的SQS是这些代码的同构类的完全不变量。我们根据GL-等价性（类似于F^r置换的EA-型等价性）得到了所提出码的SQS的自同构群的点传递性的一个判据。基于这些结果，我们提出了一个新的构造协调传递和邻居传递扩展完美码。
英文摘要：
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 SQS of these codes 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 F^r). Based on these results we suggest a new construction for coordinate transitive and neighbor transitive extended perfect codes.
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