TY - JOUR

T1 - Coordinate transitivity of a class of extended perfect codes and their SQS

AU - Mogilnykh, I. Yu

AU - Solov'eva, F. I.

N1 - Funding Information: Mogilnykh, I.Yu., Solov'eva, F.I., Coordinate transitivity of a class of extended perfect codes and their SQS. © 2020 Mogilnykh I.Yu., Solov'eva F.I. This work was supported by the Ministry of Science and Higher Education of Russia (agreement No. 075-02-2020-1479/1). Received March, 30, 2020, published September, 14, 2020.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - concatenation construction

KW - coordinate transitive code

KW - extended perfect code

KW - isomorphism problem

KW - neighbor transitive code

KW - regular subgroup

KW - transitive action

KW - transitive code

KW - transitive Steiner quadruple system

UR - http://www.scopus.com/inward/record.url?scp=85099397159&partnerID=8YFLogxK

U2 - 10.33048/semi.2020.17.101

DO - 10.33048/semi.2020.17.101

M3 - Article

AN - SCOPUS:85099397159

VL - 17

SP - 1451

EP - 1462

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -