diff --git a/pyrival/linear_algebra/xor_basis.py b/pyrival/linear_algebra/xor_basis.py
new file mode 100644
index 0000000..edacd61
--- /dev/null
+++ b/pyrival/linear_algebra/xor_basis.py
@@ -0,0 +1,35 @@
+class XorBasis:
+    " Linear basis for xor "
+        
+    def __init__(self):
+        self.basis = []
+    
+    def insert(self, x):
+        "Adds x to the basis if it is not redundant. Returns true if x is added to the basis"
+        x = self._reduce(x)
+        if x:
+            self.basis.append(x)
+        return x!=0
+    
+    def _reduce(self, x):
+        for b in self.basis:
+            x = min(x, x ^ b)
+        return x
+    
+    def __len__(self):
+        return len(self.basis)
+    
+    def __contains__(self, x):
+        " Returns true if x can be represented as xor of some already inserted elements"
+        return self._reduce(x)==0
+    
+    def __repr__(self):
+        " Prints the basis in descending order "
+        self.basis.sort(reverse=True)
+        bit_length = max(self.basis).bit_length()
+        repr_str = ""
+        repr_str += "Basis:"
+        for b in self.basis:
+            repr_str+='\n'
+            repr_str+= bin(b)[2:].zfill(bit_length)
+        return repr_str
\ No newline at end of file