Table1: Classification of periodic Golay pairs of length v, PGP(v)
v Number of equivalence classes  List of representatives of each equivalence class
2 1 [[-1,1], [1,1]]
4 1 [[-1,1,1,1], [-1,1,1,1]]
8 2

[ [ -1,-1, -1, 1, -1, 1, 1, 1 ], [ -1, 1, 1, -1, 1, 1, 1, 1 ] ],
[ [ -1, -1, -1, 1, 1, -1, 1, 1 ], [ -1, 1, -1, 1, 1, 1, 1, 1 ] ]

10 1

[ [ -1, -1, 1, 1, 1, 1, -1, 1, -1, 1 ], [ -1, -1, 1, 1, 1, 1, 1, -1, 1, 1 ]]

16 11 v16reps.txt
20 34 v20reps.txt
26 53 v26reps.txt
32 838 v32reps.txt
34 373 v34reps.txt
40 ≥ 323 v40reps.txt

 

Table 2: PBD(v, {ka, kb}, λ) classifications with automorphism group Cv corresponding to the existence of PGP(v)
v {ka, kb} r λ Number of isomorphism classes  List of representatives of each isomorphism class
2 [1,0]
[2,1]
1
3
0
2
1
1
blocks:=[ [ 1 ], [ 2 ] ]
blocks:=[ [ 1 ], [ 1, 2 ], [ 1, 2 ], [ 2 ] ]
4 [1,1]
[3,1]
[3,3]
2
4
6
0
2
4
1
1
1
PBDs_v4_r2.txt
PBDs_v4_r4.txt
PBDs_v4_r6.txt
8 [4,2]
[6,4]
6
10
2
6
2
2
PBDs_v8_r6.txt
PBDs_v8_r10.txt
10 [4,3]
[6,3]
[7,4]
[7,6]
7
9
11
13
2
4
6
8
2
2
2
2
PBDs_v10_r7.txt
PBDs_v10_r9.txt
PBDs_v10_r11.txt
PBDs_v10_r13.txt
16 [6,6]
[10,6]
[10,10]
12
16
20
4
8
12
16
30
16
PBDs_v16_r12.txt
PBDs_v16_r16.txt
PBDs_v16_r20.txt
20 [9,7]
[11,7]
[13,9]
[13,11]
16
18
22
24
6
8
12
14
112
112
112
112
PBDs_v20_r16.txt
PBDs_v20_r18.txt
PBDs_v20_r22.txt
PBDs_v20_r24.txt
26 [11,10]
[15,10]
[16,11]
[16,15]
21
25
27
31
8
12
14
18
204
204
204
204
PBDs_v26_r21.txt
PBDs_v26_r25.txt
PBDs_v26_r27.txt
PBDs_v26_r31.txt
32 [16,12]
[20,16]
28
36
12
20
5104
5104
PBDs_v32_r28.txt
PBDs_v32_r36.txt
34 [16,13]
[18,13]
[21,16]
[21,18]
29
31
37
39
12
14
20
22
1464
1464
1464
1464
PBDs_v34_r29.txt
PBDs_v34_r31.txt
PBDs_v34_r37.txt
PBDs_v34_r39.txt
40 [18,16]
[22,16]
[24,18]
[24,22]
34
38
42
46
14
18
22
26
≥ 565


PBDs_v40_r34.txt