Coordinate transitivity of a class of extended perfect codes and their SQS

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Abstract

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 GL-equivalence (similar to EA-type equivalence for permutations of Fr). Based on these results we suggest a new construction for coordinate transitive and neighbor transitive extended perfect codes.

Original languageEnglish
Pages (from-to)1451-1462
Number of pages12
JournalSiberian Electronic Mathematical Reports
Volume17
DOIs
Publication statusPublished - 2020

Keywords

  • concatenation construction
  • coordinate transitive code
  • extended perfect code
  • isomorphism problem
  • neighbor transitive code
  • regular subgroup
  • transitive action
  • transitive code
  • transitive Steiner quadruple system

OECD FOS+WOS

  • 1.01 MATHEMATICS

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