Add function for checking all Hadamard matrices

Author: MatteoCati

src/sage/combinat/matrices/hadamard_matrix.py

@@ -1615,6 +1615,37 @@ def is_skew_hadamard_matrix(M, normalized=False, verbose=False):
     return is_hadamard_matrix(M, skew=True, normalized=normalized, verbose=verbose)
 
 
+def _get_all_hadamard_matrices(skew=False):
+    r"""
+    Compute all known Hadamard matrices of order `4n`, with `1 \le n \le 250`.
+
+    The Hadamard matrices are computed using :func:`hadamard_matrix` and skew
+    Hadamard matrices are computed by :func:`skew_hadamard_matrix`.
+
+    Note that all skew and non-skew Hadamard matrices of order `\le 1000` for
+    which a construction is known are implemented in SageMath.
+
+    INPUT:
+
+    - ``skew`` -- boolean (default: ``False``); whether the matrices should be skew
+
+    OUTPUT:
+
+    The output is a list which at index `n` contain the (skew) Hadamard matrix
+    of order `4(n+1)`, or ``None` if a construction for such matrix is not yet
+    known.
+    """
+    unknown_hadamard = [668, 716, 892]
+    unknown_skew_hadamard = [356, 404, 428, 476, 596, 612, 668, 708, 712, 716,
+                             764, 772, 804, 808, 820, 836, 856, 892, 900, 916,
+                             932, 940, 952, 980, 996]
+
+    if skew:
+        return [None if 4*n in unknown_skew_hadamard else skew_hadamard_matrix(4*n) for n in range(1, 251)]
+    else:
+        return [None if 4*n in unknown_hadamard else hadamard_matrix(4*n) for n in range(1, 251)]
+
+
 @matrix_method
 def hadamard_matrix(n, existence=False, check=True):
     r"""