Data from:
Hiroyuki Ohmori
Classification of weighing matrices of small orders
Hiroshima Mathematical Journal, Volume 22, No.1, March 1992

Lemma 3.1 : The unique weighing matrix of Type C_5 up to equivalence.

(U1,1) =
1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 - - - - 0 0 0 0 0 0
1 1 - - 1 1 - - 0 0 0 0 0 0
1 1 - - - - 1 1 0 0 0 0 0 0
1 - 0 0 0 0 0 0 1 1 1 1 1 1
- 1 0 0 0 0 0 0 - - 1 1 1 1
- 1 0 0 0 0 0 0 1 1 - 1 - 1
1 - 0 0 0 0 0 0 - - - 1 - 1
0 0 1 - 0 0 0 0 - 1 1 - - 1
0 0 - 1 0 0 0 0 1 - 1 - - 1
0 0 0 0 1 - 1 - 0 0 - - 1 1
0 0 0 0 - 1 - 1 0 0 - - 1 1
0 0 - 1 1 - - 1 - 1 0 0 0 0
0 0 - 1 - 1 1 - - 1 0 0 0 0

Lemma 3.2 : There are three inequivalent feasible matrices of Type C_7.

P1_7 =

1 1 1 1 1 1
- - 1 1 1 1
1 1 - - 1 1
- - - - 1 1
0 0 - 1 - 1
0 0 1 - - 1
- 1 0 0 - 1
1 - 0 0 - 1
- 1 - 1 0 0
1 - - 1 0 0

P2_7 =

1 1 1 1 1 1
- - 1 1 1 1
- 1 - 1 - 1
1 - 1 - - 1
0 0 - - 1 1
0 0 - - 1 1
1 1 0 0 - 1
- - 0 0 - 1
1 - - 1 0 0
1 - - 1 0 0

P3_7 =

1 1 1 1 1 1
- - 1 1 1 1
- 1 - - 1 1
1 - - - 1 1
0 0 - 1 - 1
0 0 1 - - 1
1 1 0 0 - 1
- - 0 0 - 1
- 1 - 1 0 0
1 - - 1 0 0

Lemma 3.3 : There are four inequivalent matrices of Type C_15

P1_15 =

1 1 1 1 1 1
- - 1 1 1 1
1 - - 1 - 1
1 - 1 - - 1
0 0 - - 1 1
0 0 - - 1 1
- 1 0 0 - 1
- 1 0 0 - 1
0 0 - 1 0 0
0 0 - 1 0 0
1 1 0 0 0 0
1 1 0 0 0 0

P2_15 =

1 1 1 1 1 1
- - 1 1 1 1
- 1 - - 1 1
1 - - - 1 1
0 0 - 1 - 1
0 0 1 - - 1
1 1 0 0 - 1
- - 0 0 - 1
0 0 - 1 0 0
0 0 - 1 0 0
- 1 0 0 0 0
- 1 0 0 0 0

P3_15 =

1 1 1 1 1 1
- - - - 1 1
- - 1 1 - 1
1 1 - - - 1
0 0 - 1 1 1
0 0 1 - 1 1
- 1 0 0 - 1
1 - 0 0 - 1
0 0 - 1 0 0
0 0 - 1 0 0
- 1 0 0 0 0
- 1 0 0 0 0

P4_15 =

1 1 1 1 1 1
- - 1 1 1 1
1 1 - - 1 1
- - - - 1 1
0 0 - 1 - 1
0 0 1 - - 1
- 1 0 0 - 1
1 - 0 0 - 1
0 0 - 1 0 0
0 0 - 1 0 0
- 1 0 0 0 0
- 1 0 0 0 0

Lemma 3.4 : There are five inequivalent matrices of Type C_17

P1_17 =

1 1 1 1 1 1
- - - - 1 1
0 0 - 1 - 1
0 0 1 - - 1
- 1 0 0 - 1
1 - 0 0 - 1
- - 1 1 0 0
- - 1 1 0 0
- 1 - 1 0 0
1 - - 1 0 0
0 0 0 0 1 1
0 0 0 0 1 1

P2_17 =

1 1 1 1 1 1
- - 1 1 - 1
0 0 - - 1 1
- - 0 0 1 1
0 0 - - - 1
1 1 0 0 - 1
- 1 - 1 0 0
- 1 - 1 0 0
1 - - 1 0 0
1 - - 1 0 0
0 0 0 0 1 1
0 0 0 0 - 1

P3_17 =

1 1 1 1 1 1
- - 1 1 1 1
0 0 - - 1 1
0 0 - - 1 1
- 1 0 0 - 1
1 - 0 0 - 1
1 1 - 1 0 0
- 1 - 1 0 0
- 1 - 1 0 0
1 - - 1 0 0
0 0 0 0 - 1
0 0 0 0 - 1

P4_17 =

1 1 1 1 1 1
- - 1 1 1 1
0 0 - - 1 1
0 0 - - 1 1
1 1 0 0 - 1
- - 0 0 - 1
- 1 - 1 0 0
- 1 - 1 0 0
1 - - 1 0 0
1 - - 1 0 0
0 0 0 0 - 1
0 0 0 0 - 1

P5_17 =

1 1 1 1 1 1
- - 1 1 1 1
0 0 - - 1 1
0 0 - 1 - 1
- 1 0 - 0 1
1 - 0 - 0 1
- 1 - 0 1 0
1 - - 0 1 0
1 1 - 1 0 0
- - - 1 0 0
0 0 0 0 - 1
0 0 0 0 - 1

Lemma 3.5 : There are two inequivalent matrices of Type C_18.

P1_18 =

1 1 1 1 1 1
0 0 0 0 1 1
0 0 - - 1 1
- - 0 0 1 1
0 1 0 1 - 1
1 0 0 - - 1
0 - 1 0 - 1
- 0 - 0 - 1
- 1 - 1 0 0
1 - - 1 0 0
- - 1 1 0 0
1 - - 1 0 0

P2_18 =

1 1 1 1 1 1
0 0 0 0 - 1
0 0 - 1 1 1
0 - 0 - 1 1
- 0 0 - 1 1
0 1 1 0 - 1
- 0 - 0 - 1
1 - 0 0 - 1
- - 1 1 0 0
- - 1 1 0 0
- 1 - 1 0 0
1 - - 1 0 0

Lemma 3.6 : There are 19 inequivalent feasible matrices of Type C_19.

P1_19 =

0 0 1 1 1 1
0 0 1 1 1 1
0 0 - - 1 1
0 0 - - 1 1
1 1 0 0 - 1
1 1 0 0 - 1
- - 0 0 - 1
- - 0 0 - 1
- 1 - 1 0 0
- 1 - 1 0 0
1 - - 1 0 0
1 - - 1 0 0

P2_19 =

0 0 1 1 1 1
0 0 1 1 1 1
0 0 - - 1 1
0 0 - - 1 1
1 1 0 0 - 1
- 1 0 0 - 1
1 - 0 0 - 1
- - 0 0 - 1
1 1 - 1 0 0
- 1 - 1 0 0
1 - - 1 0 0
- - - 1 0 0

P3_19 =

0 0 1 1 1 1
0 0 - 1 1 1
0 0 1 - 1 1
0 0 - - 1 1
1 1 0 0 - 1
- 1 0 0 - 1
1 - 0 0 - 1
- - 0 0 - 1
1 1 1 1 0 0
- - 1 1 0 0
- 1 - 1 0 0
1 - - 1 0 0

P4_19 =

0 0 1 1 1 1
0 0 - 1 1 1
0 1 0 - 1 1
0 - 0 - 1 1
1 0 1 0 - 1
1 0 - 0 - 1
- 1 0 0 - 1
- - 0 0 - 1
1 1 1 1 0 0
- - 1 1 0 0
- 1 - 1 0 0
1 - - 1 0 0

P5_19 =

0 0 1 1 1 1
0 1 0 1 1 1
0 0 - - 1 1
0 - 0 - 1 1
1 0 1 0 - 1
- 0 - 0 - 1
- 1 0 0 - 1
1 - 0 0 - 1
1 1 - 1 0 0
- - - 1 0 0
- - 1 1 0 0
1 - - 1 0 0

P6_19 =

0 0 1 1 1 1
0 1 0 1 1 1
0 0 - - 1 1
0 - 0 - 1 1
1 0 1 0 - 1
- 0 - 0 - 1
- 1 0 0 - 1
1 - 0 0 - 1
1 1 - 1 0 0
- - - 1 0 0
- - 1 1 0 0
1 - - 1 0 0

P7_19 =

0 0 1 1 1 1
0 0 - - 1 1
1 1 0 0 1 1
- - 0 0 1 1
0 0 - 1 - 1
0 0 1 - - 1
- 1 0 0 - 1
1 - 0 0 - 1
1 1 1 1 0 0
- - 1 1 0 0
- 1 - 1 0 0
1 - - 1 0 0

P8_19 =

0 0 1 1 1 1
0 0 - - 1 1
1 1 0 0 1 1
- - 0 0 1 1
0 1 0 1 - 1
0 - 0 - - 1
1 0 1 0 - 1
- 0 - 0 - 1
- 1 - 1 0 0
1 - - 1 0 0
- - 1 1 0 0
1 - - 1 0 0

P9_19 =

0 0 1 1 1 1
0 0 - - 1 1
1 1 0 0 1 1
- - 0 0 1 1
0 1 0 1 - 1
0 - 0 - - 1
- 0 1 0 - 1
1 0 - 0 - 1
- 1 - 1 0 0
1 - - 1 0 0
1 - 1 1 0 0
- - - 1 0 0

P10_19 =

0 0 1 1 1 1
0 0 - - 1 1
1 1 0 0 1 1
- - 0 0 1 1
0 0 - 1 - 1
0 0 1 - - 1
- 1 0 0 - 1
1 - 0 0 - 1
- 1 1 1 0 0
1 - 1 1 0 0
1 1 - 1 0 0
- - - 1 0 0

P11_19 =

0 0 1 1 1 1
0 1 0 - 1 1
1 0 - 0 1 1
- - 0 0 1 1
0 0 1 1 - 1
0 1 0 - - 1
1 0 - 0 - 1
- - 0 0 - 1
- 1 - 1 0 0
1 - - 1 0 0
1 1 1 1 0 0
- 1 - 1 0 0

P12_19 =

0 0 1 1 1 1
0 1 0 - 1 1
1 0 - 0 1 1
- - 0 0 1 1
0 0 - 1 - 1
0 - 0 - - 1
1 0 1 0 - 1
- 1 0 0 - 1
1 1 1 1 0 0
- - 1 1 0 0
- 1 - 1 0 0
1 - - 1 0 0

P13_19 =

0 0 1 1 1 1
0 1 0 - 1 1
1 0 - 0 1 1
- - 0 0 1 1
0 0 - 1 - 1
0 - 0 - - 1
1 0 1 0 - 1
- 1 0 0 - 1
- 1 1 1 0 0
1 - 1 1 0 0
1 1 - 1 0 0
- - - 1 0 0

P14_19 =

0 0 1 1 1 1
0 1 0 1 1 1
0 0 - - 1 1
0 - 0 1 - 1
1 0 1 0 - 1
- 0 - 0 - 1
1 1 0 - 0 1
- - 0 - 0 1
- - 1 0 1 0
1 - - 0 1 0
- 1 - 1 0 0
1 - - 1 0 0

P15_19 =

0 0 1 1 1 1
0 1 0 1 1 1
0 0 - - 1 1
0 - 0 1 - 1
1 0 1 0 - 1
- 0 - 0 - 1
- 1 0 - 0 1
1 - 0 - 0 1
- - 1 0 1 0
1 - - 0 1 0
1 1 - 1 0 0
- - - 1 0 0

P16_19 =

0 0 1 1 1 1
0 1 0 - 1 1
1 0 - 0 1 1
0 1 0 1 - 1
0 0 1 - - 1
- 0 - 0 - 1
- - 0 1 0 1
1 - 0 - 0 1
- - 1 0 1 0
- 1 - 0 1 0
1 1 1 1 0 0
1 - - 1 0 0

P17_19 =

0 0 1 1 1 1
0 1 0 - 1 1
1 0 - 0 1 1
0 1 0 1 - 1
0 0 1 - - 1
- 0 - 0 - 1
- - 0 1 0 1
1 - 0 - 0 1
- 1 1 0 1 0
- - - 0 1 0
1 - 1 1 0 0
1 1 - 1 0 0

P18_19 =

0 0 1 1 1 1
0 0 - - 1 1
0 1 0 1 1 1
0 - 0 1 - 1
1 1 0 0 - 1
- - 0 0 - 1
1 0 1 - 0 1
- 0 - - 0 1
- - 1 0 1 0
1 - - 0 1 0
- 1 - 1 0 0
1 - - 1 0 0

P19_19 =

0 0 1 1 1 1
0 0 - - 1 1
0 1 0 1 1 1
0 - 0 1 - 1
1 1 0 0 - 1
- - 0 0 - 1
- 0 1 - 0 1
1 0 - - 0 1
1 - 1 0 1 0
- - - 0 1 0
- 1 - 1 0 0
1 - - 1 0 0

Theorem 3.5 : There are four inequivalent feasible matrices of
Type C_24

P1_24 =

1 1 1 1 1 1
- 0 - 0 1 1
- 0 1 0 - 1
0 - - 1 0 1
0 - 1 - 0 1
1 1 - 0 0 1
- - 0 1 1 0
1 - 0 - 1 0
- 1 1 0 1 0
1 - 1 1 0 0
0 0 0 0 - 1
0 0 0 - 0 1
0 0 0 - 1 0

P2_24 =

1 1 1 1 1 1
0 0 - 1 1 1
0 - 0 - 1 1
0 1 0 - - 1
1 - 0 0 - 1
- - 1 0 0 1
- 1 - 0 0 1
- 0 1 - 1 0
1 0 - - 1 0
- - - 1 0 0
0 0 0 0 - 1
0 0 0 - 1 0
- 1 0 0 0 0

P3_24 =

1 1 1 1 1 1
0 0 - 1 - 1
0 - 0 - 1 1
0 1 0 - - 1
1 - 0 0 - 1
- - 1 0 0 1
- 1 - 0 0 1
- 0 - 1 1 0
1 0 - - 1 0
1 - - 1 0 0
0 0 0 0 1 1
0 0 1 1 0 0
1 1 0 0 0 0

P4_24 =

1 1 1 1 1 1
0 0 1 - - 1
0 - 0 - 1 1
0 1 0 1 - 1
- 1 0 0 - 1
- 1 - 0 0 1
1 - - 0 0 1
- 0 - 1 1 0
- 0 1 - 1 0
- - 1 1 0 0
0 0 0 0 1 1
0 0 1 1 0 0
1 1 0 0 0 0

Theorem 3.6 : There are two inequivalent feasible matrices of Type
C_25.

P1_25 =

0 0 1 1 1 1
1 1 0 0 1 1
- 1 0 0 - 1
0 - - 1 0 1
0 1 - - 0 1
- - 0 - 0 1
1 - 1 0 0 1
- 0 1 - 1 0
1 0 - - 1 0
- 1 0 1 1 0
- - - 0 1 0
0 0 0 0 - 1
0 0 - 1 0 0

P2_25 =

0 0 1 1 1 1
1 1 0 0 - 1
- - 0 0 - 1
0 1 - 1 0 1
0 - - - 0 1
- 1 0 - 0 1
1 - 1 0 0 1
- 0 - 1 1 0
- 0 1 - 1 0
1 1 0 - 1 0
1 - - 0 1 0
0 0 0 0 1 1
0 0 1 1 0 0