Indeterminates and Incidence Matrices

Combinatorics ◽  
1975 ◽  
pp. 3-17
Author(s):  
H. J. Ryser
Keyword(s):  
Incidence Matrices

scholarly journals Maximal Arcs, Codes, and New Links Between Projective Planes of Order 16

10.37236/9008 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Mustafa Gezek ◽  
Rudi Mathon ◽  
Vladimir D. Tonchev
Keyword(s):  
Minimum Distance ◽  
Linear Codes ◽  
Projective Planes ◽  
Upper And Lower Bounds ◽  
Dual Codes ◽  
Binary Linear Codes ◽  
Incidence Matrices ◽  
Maximal Arc ◽  
Maximal Arcs ◽  
Even Order

In this paper we consider binary linear codes spanned by incidence matrices of Steiner 2-designs associated with maximal arcs in projective planes of even order, and their dual codes. Upper and lower bounds on the 2-rank of the incidence matrices are derived. A lower bound on the minimum distance of the dual codes is proved, and it is shown that the bound is achieved if and only if the related maximal arc contains a hyperoval of the plane. The  binary linear codes of length 52 spanned by the incidence matrices of 2-$(52,4,1)$ designs associated with previously known and some newly found maximal arcs of degree 4 in projective planes of order 16 are analyzed and classified up to equivalence. The classification shows that some designs associated with maximal arcs in nonisomorphic planes generate equivalent codes. This phenomenon establishes new links between several of the known planes. A conjecture concerning the codes of maximal arcs in $PG(2,2^m)$ is formulated.

scholarly journals An inequality for incidence matrices

1959 ◽  
Vol 10 (2) ◽  
pp. 216-216 ◽  
Author(s):  
J. R. Isbell
Keyword(s):  
Incidence Matrices

On Integer Matrices and Incidence Matrices of Certain Combinatorial Configurations, III: Rectangular Matrices

1966 ◽  
Vol 18 ◽  
pp. 9-17
Author(s):  
Kulendra N. Majindar
Keyword(s):  
Necessary Conditions ◽  
Block Designs ◽  
Incomplete Block ◽  
Incidence Matrices ◽  
Balanced Incomplete Block Designs ◽  
Balanced Incomplete Block ◽  
Definition Of ◽  
Combinatorial Configurations

In this paper, we give a connection between incidence matrices of affine resolvable balanced incomplete block designs and rectangular integer matrices subject to certain arithmetical conditions. The definition of these terms can be found in paper II of this series or in (2). For some necessary conditions on the parameters of affine resolvable balanced incomplete block designs and their properties see (2).

Cyclic Incidence Matrices

1951 ◽  
Vol 3 ◽  
pp. 495-502 ◽  
Author(s):  
Marshall Hall ◽  
H. J. Ryser
Keyword(s):  
Combinatorial Problem ◽  
Incidence Matrices

Let it be required to arrange v elements into v sets such that each set contains exactly k distinct elements and such that each pair of sets has exactly λ elements in common (0 < λ < k < v). This problem we refer to as the v, k,λ combinatorial problem.

scholarly journals Incidence Matrices and Linear Graphs

1959 ◽  
Vol 8 (5) ◽  
pp. 827-835 ◽  
Author(s):  
L. Auslander ◽  
H. Trent
Keyword(s):  
Incidence Matrices ◽  
Linear Graphs

Geometries and Incidence Matrices

1955 ◽  
Vol 62 (7P2) ◽  
pp. 25-31 ◽  
Author(s):  
H. J. Ryser
Keyword(s):  
Incidence Matrices

scholarly journals Asymptotic enumeration of incidence matrices

2006 ◽  
Vol 42 ◽  
pp. 59-70 ◽  
Author(s):  
Peter Cameron ◽  
Thomas Prellberg ◽  
Dudley Stark
Keyword(s):  
Asymptotic Enumeration ◽  
Incidence Matrices

Ranks of incidence matrices of Steiner triple systems

1978 ◽  
Vol 163 (3) ◽  
pp. 251-259 ◽  
Author(s):  
Jean Doyen ◽  
Xavier Hubaut ◽  
Monique Vandensavel
Keyword(s):  
Steiner Triple Systems ◽  
Incidence Matrices ◽  
Triple Systems

scholarly journals Incidence matrices of finite attenuated spaces and class dimension of association schemes

2014 ◽  
Vol 315-316 ◽  
pp. 42-46 ◽  
Author(s):  
Jun Guo ◽  
Fenggao Li ◽  
Kaishun Wang
Keyword(s):  
Association Schemes ◽  
Incidence Matrices
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