Characterization of the association schemes of Hermitian forms over GF(22)

A. A. Ivanov; S. V. Shpectorov

doi:10.1007/BF02424310

Characterization of the association schemes of Hermitian forms over GF(2²)

A. A. Ivanov^*, S. V. Shpectorov

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

It is shown that an association scheme Y=(X, {R_i}_0≤i≤d), in which the parameters coincide with those of the scheme Her(d, 2) of Hermitian forms in d-dimensional space over GF(2²), is isomorphic to Her(d, 2). A principal role in the proof is played by a theorem by P. Terwilliger on the number of 4-vertex configurations of a given type in (P and Q)-polynomial association schemes. Some partial results are obtained in the case of an arbitrary finite field.

Original language	English
Pages (from-to)	23-33
Number of pages	11
Journal	Geometriae Dedicata
Volume	30
Issue number	1
DOIs	https://doi.org/10.1007/BF02424310
Publication status	Published - Apr 1989

ASJC Scopus subject areas

Geometry and Topology

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10.1007/BF02424310

Cite this

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abstract = "It is shown that an association scheme Y=(X, {Ri}0≤i≤d), in which the parameters coincide with those of the scheme Her(d, 2) of Hermitian forms in d-dimensional space over GF(22), is isomorphic to Her(d, 2). A principal role in the proof is played by a theorem by P. Terwilliger on the number of 4-vertex configurations of a given type in (P and Q)-polynomial association schemes. Some partial results are obtained in the case of an arbitrary finite field.",

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AB - It is shown that an association scheme Y=(X, {Ri}0≤i≤d), in which the parameters coincide with those of the scheme Her(d, 2) of Hermitian forms in d-dimensional space over GF(22), is isomorphic to Her(d, 2). A principal role in the proof is played by a theorem by P. Terwilliger on the number of 4-vertex configurations of a given type in (P and Q)-polynomial association schemes. Some partial results are obtained in the case of an arbitrary finite field.

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