scholarly journals On the Classification of Splitting (v, u×c, λ) BIBDs

2018 ◽  
Vol 18 (5) ◽  
pp. 87-94
Author(s):  
Stela Zhelezova
Keyword(s):  
Block Designs ◽  
Incomplete Block ◽  
Authentication Codes ◽  
Balanced Incomplete Block Designs ◽  
Splitting Authentication Codes ◽  
Balanced Incomplete Block

Abstract The (v, u×c, λ)-splitting balanced incomplete block designs correspond to c-splitting authentication codes. We classify splitting balanced incomplete block designs with definite parameters.

Classification of resolvable balanced incomplete block designs — the unitals on 28 points

2009 ◽  
Vol 59 (2) ◽  
Author(s):  
Petteri Kaski ◽  
Patric Östergård
Keyword(s):  
Block Designs ◽  
Incomplete Block ◽  
Doctoral Thesis ◽  
Parallel Class ◽  
Balanced Incomplete Block Designs ◽  
Balanced Incomplete Block

AbstractApproaches for classifying resolvable balanced incomplete block designs (RBIBDs) are surveyed. The main approaches can roughly be divided into two types: those building up a design parallel class by parallel class and those proceeding point by point. With an algorithm of the latter type — and by refining ideas dating back to 1917 and the doctoral thesis by Pieter Mulder — it is shown that the list of seven known resolutions of 2-(28, 4, 1) designs is complete; these objects are also known as the resolutions of unitals on 28 points.

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