scholarly journals Cyclotomic Trace Codes

Algorithms ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 168
Author(s):  
Dean Crnković ◽  
Andrea Švob ◽  
Vladimir D. Tonchev
Keyword(s):  
Quantum Codes ◽  
Strongly Regular Graphs ◽  
Block Designs ◽  
Regular Graphs ◽  
Combinatorial Structures ◽  
Trace Codes ◽  
Strongly Regular ◽  
Projective Codes

A generalization of Ding’s construction is proposed that employs as a defining set the collection of the sth powers ( s ≥ 2 ) of all nonzero elements in G F ( p m ) , where p ≥ 2 is prime. Some of the resulting codes are optimal or near-optimal and include projective codes over G F ( 4 ) that give rise to optimal or near optimal quantum codes. In addition, the codes yield interesting combinatorial structures, such as strongly regular graphs and block designs.

Strongly Regular Graphs Derived from Combinatorial Designs

1970 ◽  
Vol 22 (3) ◽  
pp. 597-614 ◽  
Author(s):  
J. M. Goethals ◽  
J. J. Seidel
Keyword(s):  
Strongly Regular Graph ◽  
Hadamard Matrices ◽  
Latin Squares ◽  
Discrete Mathematics ◽  
Strongly Regular Graphs ◽  
Block Designs ◽  
Regular Graphs ◽  
Geometric Configurations ◽  
Strongly Regular ◽  
Definition Of

Several concepts in discrete mathematics such as block designs, Latin squares, Hadamard matrices, tactical configurations, errorcorrecting codes, geometric configurations, finite groups, and graphs are by no means independent. Combinations of these notions may serve the development of any one of them, and sometimes reveal hidden interrelations. In the present paper a central role in this respect is played by the notion of strongly regular graph, the definition of which is recalled below.In § 2, a fibre-type construction for graphs is given which, applied to block designs withλ= 1 and Hadamard matrices, yields strongly regular graphs. The method, although still limited in its applications, may serve further developments. In § 3 we deal with block designs, first considered by Shrikhande[22],in which the number of points in the intersection of any pair of blocks attains only two values.

scholarly journals On Some Combinatorial Structures Constructed from the Groups , , and

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Dean Crnković ◽  
Vedrana Mikulić Crnković
Keyword(s):  
Automorphism Group ◽  
Conjugacy Classes ◽  
Maximal Subgroups ◽  
Simple Groups ◽  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Combinatorial Structures ◽  
Full Automorphism Group ◽  
Incidence Structures ◽  
Strongly Regular

We describe a construction of primitive 2-designs and strongly regular graphs from the simple groups , and . The designs and the graphs are constructed by defining incidence structures on conjugacy classes of maximal subgroups of , and . In addition, from the group , we construct 2-designs with parameters and having the full automorphism group isomorphic to .

On extensions of small strongly regular graphs with eigenvalue 3

2015 ◽  
Vol 92 (1) ◽  
pp. 482-486
Author(s):  
A. A. Makhnev ◽  
D. V. Paduchikh
Keyword(s):  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Strongly Regular

On triple systems and strongly regular graphs

2012 ◽  
Vol 119 (7) ◽  
pp. 1414-1426 ◽  
Author(s):  
Majid Behbahani ◽  
Clement Lam ◽  
Patric R.J. Östergård
Keyword(s):  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Triple Systems ◽  
Strongly Regular
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