Abstract
It follows from Delsarte theory that the Witt 4-(11, 5, 1) design gives rise to a Q-polynomial association scheme \({\mathcal {W}}\) defined on the set of its blocks. In this note we show that \({\mathcal {W}}\) is unique, i.e., defined up to isomorphism by its parameters.
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References
Bannai E., Bannai E., Bannai H.: Uniqueness of certain association schemes. Eur. J. Combin. 25, 261–267 (2004).
Bannai E., Ito T.: Algebraic Combinatorics I: Association Schemes. Benjamin/Cummings, Menlo Park (1984).
Beth T., Jungnickel D.: Mathieu groups, with designs, and Golay codes. Lecture Notes Math. 893, 157–169 (1981).
Brouwer A.E., Cohen A.E., Neumaier A.: Distance-regular graphs. Springer, Berlin (1989). xviii+495.
Chang L.C.: The uniqueness and nonuniqueness of the triangular association scheme. Sci. Record 3, 604–613 (1959).
Delsarte P.: An algebraic approach to the association schemes of coding theory. Philips Research Reports Supplements, No. 10 (1973).
Gavrilyuk A.L., Vidali J., Williford J.S.: On few-class \(Q\)-polynomial association schemes: feasible parameters and nonexistence results. ARS Math. Contemp. 20(1), 103–127 (2021).
van Dam E.R.: Three-class association schemes. J. Alg. Combin. 10, 69–107 (1999).
Williford J.S.: Tables of feasible parameter sets for primitive 3-class \(Q\)-polynomial association schemes. https://jaanos.github.io/tables/.
Acknowledgements
The authors would like to thank the reviewers for valuable comments. The research of Alexander Gavrilyuk is supported by JSPS KAKENHI Grant Number 22K03403. The research of Sho Suda is supported by JSPS KAKENHI Grant Numbers 18K03395 and 22K03410.
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Communicated by A. Pott.
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Gavrilyuk, A.L., Suda, S. Uniqueness of an association scheme related to the Witt design on 11 points. Des. Codes Cryptogr. 92, 205–209 (2024). https://doi.org/10.1007/s10623-023-01303-8
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DOI: https://doi.org/10.1007/s10623-023-01303-8