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40 lines
743 B
Python
40 lines
743 B
Python
K = GF(5)
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n = 5
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d = 3
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# Ambient vector space
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V = VectorSpace(K, n)
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assert V([1, 1, 0, 0, 0]).hamming_weight() == 2
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def is_codespace(W, d):
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return all(v.hamming_weight() >= d for v in W if v != 0)
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done = False
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for j in range(2, n+1):
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print(f"trying k={j}")
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for W in V.subspaces(j):
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if is_codespace(W, d):
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C = W
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done = True
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break
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if done:
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break
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k = C.dimension()
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E = V.subspace([
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[1, 0, 0, 0, 0],
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[0, 1, 0, 0, 0],
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])
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#assert C.dimension() == k
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assert E.dimension() == d - 1
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assert C.intersection(E).dimension() == 0
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assert C.dimension() + E.dimension() == (C + E).dimension()
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# But C + E are both subspaces of V which is dim N
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assert (C + E).dimension() <= n
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