Add skew SDS of size 37 and 43

src/doc/en/reference/references/index.rst

@@ -2032,11 +2032,16 @@ REFERENCES:
              and some constructions of de Luca and Rauzy*,
              Theoret. Comput. Sci.  255 (2001) 539--553.
 
-.. [Djo1992] \D. Đoković.
+.. [Djo1992a] \D. Đoković.
              *Construction of some new Hadamard matrices*,
              Bulletin of the Australian Mathematical Society 45(2) (1992): 327-332.
              :doi:`10.1017/S0004972700030185`
 
+.. [Djo1992b] \D. Đoković.
+             *Skew Hadamard matrices of order 4 x 37 and 4 x 43*,
+             Journal of Combinatorial Theory, Series A 61(2) (1992): 319-321.
+             :doi:`10.1016/0097-3165(92)90029-T`
+
 .. [Djo1994] \D. Đoković.
              *Five New Orders for Hadamard Matrices of Skew Type*,
              Australasian Journal of Combinatorics  10 (1994): 259-264.

src/sage/combinat/designs/difference_family.py

@@ -1936,8 +1936,11 @@ def skew_supplementary_difference_set(n, existence=False, check=True):
     These sets are constructed from available data, as described in [Djo1994]_. The set `S_1 \subset G` is 
     always skew, i.e. `S_1 \cap (-S_1) = \emptyset` and `S_1 \cup (-S_1) = G\setminus\{0\}`.
 
-    The data for `n = 103, 151` is taken from [Djo1994]_ and the data for `n = 67, 113, 127, 157, 163, 181, 241`
-    is taken from [Djo1992]_.
+    The data is taken from:
+    
+    * `n = 103, 151`: [Djo1994]_
+    * `n = 67, 113, 127, 157, 163, 181, 241`: [Djo1992a]_
+    * `n = 37, 43`: [Djo1992b]_
     
     INPUT:
 
@@ -1991,8 +1994,11 @@ def skew_supplementary_difference_set(n, existence=False, check=True):
         True
     """
 
-
+    # If -1 is present in an index set, it means that {0} should be added to that set
     indices = {
+        37: [[0, 3, 5, 7, 9, 10], [0, 5, 6, 7, 8],
+             [1, 2, 6, 7, 9], [2, 6, 8, 9, 10]],
+        43: [[1, 2, 4], [1, 2, 4], [0, 2, 3], [3, 4, -1]],
         67:  [[0,3,5,6,9,10,13,14,17,18,20],
               [0,2,4,9,11,12,13,16,19,21],
               [1,3,6,10,11,13,14,16,20,21],
@@ -2032,6 +2038,8 @@ def skew_supplementary_difference_set(n, existence=False, check=True):
     }
 
     cosets_gens = {
+        37: [1, 2, 3, 5, 6, 9],
+        43: [1, 3, 7],
         67: [1,2,3,4,5,6,8,10,12,15,17],
         103: [1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 17, 19, 21, 23, 30],
         113: [1, 2, 3, 5, 6, 9, 10, 13],
@@ -2044,6 +2052,8 @@ def skew_supplementary_difference_set(n, existence=False, check=True):
     }
 
     H_db = {
+        37: [1, 10, -11],
+        43: [1, 4, 11, 16, 21, -2, -8],
         67: [1, 29, 37],
         103: [1, 46, 56],
         113: [1,16,28,30,49,106,109],
@@ -2058,7 +2068,10 @@ def skew_supplementary_difference_set(n, existence=False, check=True):
     def generate_set(index_set, cosets):
         S = []
         for idx in index_set:
-            S += cosets[idx]
+            if idx == -1:
+                S.append(0)
+            else:
+                S += cosets[idx]
         return S
 
 

src/sage/combinat/matrices/hadamard_matrix.py

@@ -2018,7 +2018,7 @@ def GS_skew_hadamard_smallcases(n, existence=False, check=True):
     
     Additional data is obtained from skew supplementary difference sets contained in 
     :func:`sage.combinat.designs.difference_family.skew_supplementary_difference_set`, using the 
-    construction described in [Djo1992]_.
+    construction described in [Djo1992a]_.
 
     INPUT: