Supplement: Uniqueness of certain association schemes

Eiichi Bannai, Etsuko Bannai, and Hideo Bannai.

Note: the numbering of some of the vectors may be different from the paper. Also note that numberings start from 0 and not 1. . The source code used for the calculations will also be available in the near future (we are currently cleaning it up). It is written in C++ and uses the GiNaC C++ library for the computation of the inner products.

Class 4 association scheme of 40 points in R10.

Files: c4-88.txt, c4-88ip.txt
Description: 88 vectors in R10 satisfing (1),(2),(3) or (1),(2),(3bis) and their inner products.
Files: c4-40-1.txt, c4-40ip-1.txt, c4-40-2.txt, c4-40ip-2.txt
Description: 40 vectors in R10 and their inner products

Class 3 association scheme of 64 points in R14.

Files: c3-type8-64.txt, c3-type8-64ip.txt
Description: 64 vectors for type (8) and their inner products.
Files: c3-type_2_6-160.txt, c3-type2_6-160ip.txt
Description: 160 vectors for type (2-6) and their inner products.
Files: c3-type_4_4-192.txt, c3-type_4_4-192ip.txt
Description: 192 vectors for type (4-4) and their inner products.
Files: c3-type_2_2_4a-264.txt, c3-type2_2_4a-264ip.txt, c3-type_2_2_4b-264.txt, c3-type2_2_4b-264ip.txt
Description: 264 vectors for type (2-2-4) and their inner products.
Files: c3-type_2_2_2_2-536.txt, c3-type_2_2_2_2-536ip.txt
Description: 536 vectors for type (2-2-2-2) and their inner products.
Files: c3-type_2_2_2_2-64-1.txt, c3-type_2_2_2_2-64ip-1.txt, c3-type_2_2_2_2-64-2.txt, c3-type_2_2_2_2-64ip-2.txt, c3-type_2_2_2_2-64-3.txt, c3-type_2_2_2_2-64ip-3.txt, c3-type_2_2_2_2-64-4.txt, c3-type_2_2_2_2-64ip-4.txt
Description: 64 points in R14 and their inner products
Files: c3-type_2_2_2_2-64iso.txt
Description: Isomorphism between c3-type2_2_2_2-64-1.txt and c3-type2_2_2_2-64-3.txt. The isomorphism is specified by pairs of vector indices of 0 through 63, numbered in order of c3-type2_2_2_2-64-1.txt and c3-type2_2_2_2-64-3.txt, respectively.