A non-Schurian coherent configuration on 14 points exists

For a few decades the smallest known non-Schurian coherent configuration was the association scheme on 15 points, coming from a doubly regular tournament. Last year the second author, using a computer, enumerated all coherent configurations of order up to 15. A consequence of the enumeration is that...

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Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2017-07, Vol.84 (1-2), p.203-221
Main Authors: Klin, Mikhail, Ziv-Av, Matan
Format: Article
Language:English
Subjects:
Circuits
Coding and Information Theory
Coherence
Combinatorial analysis
Computer Science
Cryptology
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Enumeration
Information and Communication
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Summary:For a few decades the smallest known non-Schurian coherent configuration was the association scheme on 15 points, coming from a doubly regular tournament. Last year the second author, using a computer, enumerated all coherent configurations of order up to 15. A consequence of the enumeration is that all coherent configurations up to 13 points are Schurian and a unique non-Schurian rank 11 coherent configuration of order 14 exists. This coherent configuration has two fibers of sizes 6 and 8, and an automorphism group of order 24 isomorphic to SL (2, 3). We provide a computer free interpretation of this new object, relying on some simple interplay between group theoretical and combinatorial arguments.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-016-0258-8