The Cyclically Resolvable Steiner Triple Systems of Order 57

被引:0
作者
Topalova, Svetlana [1 ]
Zhelezova, Stela [1 ]
机构
[1] Bulgarian Acad Sci, Inst Math & Informat, Sofia 1113, Bulgaria
关键词
Steiner triple system; cyclically resolvable; automorphism; point-cyclic resolution; anti-Pasch; anti-mitre; 5-sparse; CODES; CONSTRUCTIONS;
D O I
10.3390/math13020212
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A resolution of a Steiner triple system of order v (STS(v)) is point-cyclic if it has an automorphism permuting the points in one cycle. An STS(v) is cyclically resolvable if it has at least one point-cyclic resolution. Cyclically resolvable STS(v)s have important applications in Coding Theory. They have been classified up to v=45 and before the present work v=57 was the first open case. There are 2,353,310 cyclic STS(57)s. We establish that 155,966 of them are cyclically resolvable yielding 3,638,984 point-cyclic resolutions which we classify with respect to their automorphism groups and to the availability of some configurations.
引用
收藏
页数:13
相关论文
共 33 条
[1]  
Baicheva T., 2012, International Book Series: Information Science and Computing, P24
[2]   How to Find the Equivalence Classes in a Set of Linear Codes in Practice? [J].
Bouyuklieva, Stefka ;
Bouyukliev, Iliya .
MATHEMATICS, 2024, 12 (02)
[3]   Asymptotically optimal erasure-resilient codes for large disk arrays [J].
Chee, YM ;
Colbourn, CJ ;
Ling, ACH .
DISCRETE APPLIED MATHEMATICS, 2000, 102 (1-2) :3-36
[4]  
Colbourn C.J., 1999, Surveys in Combinatorics, P37, DOI [10.1017/CBO9780511721335.004, DOI 10.1017/CBO9780511721335.004]
[5]  
Colbourn C.J., 2007, HDB COMBINATORIAL DE, V2nd
[6]  
Colbourn C.J., 1999, OX MATH M
[7]   ANTI-MITRE STEINER TRIPLE-SYSTEMS [J].
COLBOURN, CJ ;
MENDELSOHN, E ;
ROSA, A ;
SIRAN, J .
GRAPHS AND COMBINATORICS, 1994, 10 (03) :215-224
[8]  
COLBOURN CJ, 1992, MATH COMPUT, V58, P441
[9]  
Cole F., 1922, Bulletin of the American Mathematical Society, V28, P435, DOI [10.1090/S0002-9904-1922-03599-9, DOI 10.1090/S0002-9904-1922-03599-9]
[10]   An update on the existence of Kirkman triple systems with steiner triple systems as subdesigns [J].
Dukes, Peter J. ;
Lamken, Esther R. .
JOURNAL OF COMBINATORIAL DESIGNS, 2022, 30 (08) :581-608