论文标题
协调扩展完美代码及其SQ的传递性
Coordinate transitivity of extended perfect codes and their SQS
论文作者
论文摘要
我们继续研究上一篇论文中构建的二元扩展完美推定代码，并考虑其置换自动形态（对称）组和施泰纳四倍系统。我们表明，任何此类代码的SQS的自动形态组与代码的排列自动形态组一致。特别是，这些代码的SQ是这些代码的同构类别的完全不变性。我们获得了根据GL-等效性（类似于F^r排列的EA-Type等效性），获得了拟议代码的SQ自动形态群体的点传递性标准。基于这些结果，我们提出了一个新的构造，用于坐标横向和邻居传递扩展完美代码。
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.
