$2$-arcs of maximal size in the affine and the projective Hjelmslev plane over $\mathbb Z$25
Pages: 287 - 301,
Volume 5,
Issue 2,
May 2011
doi:10.3934/amc.2011.5.287 Abstract
References
Full text (427.0K)
Related Articles
Michael Kiermaier - Institut für Mathematik, Universität Bayreuth, D-95440 Bayreuth, Germany (email)
Matthias Koch - Institut für Mathematik, Universität Bayreuth, D-95440 Bayreuth, Germany (email)
Sascha Kurz - Institut für Mathematik, Universität Bayreuth, D-95440 Bayreuth, Germany (email)
| 1 |
A. Cronheim, Dual numbers, Witt vectors, and Hjelmslev planes, Geom. Dedicata, 7 (1978), 287-302. |
|
| 2 |
L. Hemme and D. Weijand, Arcs in projektiven Hjelmslev-Ebenen, Fortgeschrittenenpraktikum, Technische Universität München, 1999. |
|
| 3 |
T. Honold and M. Kiermaier, Classification of maximal arcs in small projective Helmslev geometries, in "Proceedings of the Tenth International Workshop on Algebraic and Combinatorial Coding Theory 2006,'' (2006), 112-117. |
|
| 4 |
T. Honold and M. Kiermaier, The existence of maximal $(q^2,2)$-arcs in projective Hjelmslev planes over chain rings of odd prime characteristic, in preparation, 2011. |
|
| 5 |
T. Honold and I. Landjev, Linear codes over finite chain rings, Electr. J. Comb., 7 (2000), #R11. |
|
| 6 |
T. Honold and I. Landjev, On arcs in projective Hjelmslev planes, Discrete Math., 231 (2001), 265-278. |
|
| 7 |
T. Honold and I. Landjev, On maximal arcs in projective Hjelmslev planes over chain rings of even characteristic, Finite Fields Appl., 11 (2005), 292-304. |
|
| 8 |
M. Kiermaier, "Arcs und Codes über endlichen Kettenringen,'' Diploma thesis, Technische Universität München, 2006. |
|
| 9 |
M. Kiermaier and M. Koch, New complete $2$-arcs in the uniform projective Hjelmslev planes over chain rings of order $25$, in "Proceedings of the Sixth International Workshop on Optimal Codes and Related Topics 2009,'' (2009), 206-113. |
|
| 10 |
M. Kiermaier and A. Kohnert, Online tables of arcs in projective Hjelmslev planes, http://www.algorithm.uni-bayreuth.de |
|
| 11 |
M. Kiermaier and A. Kohnert, New arcs in projective Hjelmslev planes over Galois rings, in "Proceedings of the Fifth International Workshop on Optimal Codes and Related Topics 2007,'' (2007), 112-119. |
|
| 12 |
W. Klingenberg, Projektive und affine Ebenen mit Nachbarelementen, Math. Z., 60 (1954), 384-406. |
|
| 13 |
D. E. Knuth, Estimating the efficiency of backtrack programs, Math. Comput., 29 (1975), 121-136. |
|
| 14 |
A. Kreuzer, "Projektive Hjelmslev-Räume,'' Ph.D. thesis, Technische Universität München, 1988. |
|
| 15 |
S. Kurz, Caps in $\mathbbZ_n^2$, Serdica J. Comput., 3 (2009), 159-178. |
|
| 16 |
R. Laue, Construction of combinatorial objects - a tutorial, Bayreuther Math. Schr., 43 (1993), 53-96. |
|
| 17 |
R. Laue, Constructing objects up to isomorphism, simple $9$-designs with small parameters, in "Algebraic Combinatorics and Applications,'' Springer, Berlin, (2001), 232-260. |
|
| 18 |
H. Lüneburg, Affine Hjelmslev-Ebenen mit transitiver Translationsgruppe, Math. Z., 79 (1962), 260-288. |
|
| 19 |
F. Margot, Pruning by isomorphism in branch-and-cut, Math. Programming, 94 (2002), 71-90. |
|
| 20 |
B. McKay, Nauty, Version 2.2, http://cs.anu.edu.au/~bdm/nauty/ |
|
| 21 |
A. A. Nečaev, Finite principal ideal rings, Math. USSR-Sb., 20 (1973), 364-382. |
|
| 22 |
A. A. Nechaev, Finite rings with applications, in "Handbook of Algebra'' (ed. M. Hazewinkel), Elsevier Science Publishers, (2008), 213-320. |
|
| 23 |
R. Raghavendran, Finite associative rings, Composito Math., 21 (1969), 195-229. |
|
| 24 |
R. C. Read, Every one a winner or how to avoid isomorphism search when cataloguing combinatorial configurations, Ann. Discrete Math., 2 (1978), 107-120. |
|
| 25 |
B. Schmalz, The $t$-designs with prescribed automorphism group, new simple $6$-designs, J. Comb. Des., 1 (1993), 125-170. |
|
Go to top
|