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Hello,

Indeed there is a bug

sage: u = C((0, 0, 0, 0, 0, 0, 0))
sage: v = C((1, 0, 0, a + 1, 0, 1, 0))
sage: u in C and v in C
True

And the hamming weight of v = v-u is 3... Actually there are two algorithms in Sage and both of them fail

sage: LinearCode(G).minimum_distance(algorithm="guava")
5
sage: LinearCode(G).minimum_distance(algorithm="gap")
5

One possible reason is that it is not over a prime field.

Vincent

Hello,

Indeed there is a bug

sage: u = C((0, 0, 0, 0, 0, 0, 0))
sage: v = C((1, 0, 0, a + 1, 0, 1, 0))
sage: u in C and v in C
True

And the hamming weight of v = v-u is 3... Actually there are two algorithms in Sage and both of them fail

sage: LinearCode(G).minimum_distance(algorithm="guava")
5
sage: LinearCode(G).minimum_distance(algorithm="gap")
5

(edit: here I am wrong, the argument "guava" is considered only if the cardinality of the field is 2 or 3)

One possible reason is that it is not over a prime field.

Vincent

Hello,

Indeed there is a bug

sage: u = C((0, 0, 0, 0, 0, 0, 0))
sage: v = C((1, 0, 0, a + 1, 0, 1, 0))
sage: u in C and v in C
True

And the hamming weight of v = v-u is 3... Actually there are two algorithms in Sage and both of them fail

sage: LinearCode(G).minimum_distance(algorithm="guava")
5
sage: LinearCode(G).minimum_distance(algorithm="gap")
5

(edit: here I am wrong, the argument "guava" is considered only if the cardinality of the field is 2 or 3)

One possible reason is that it is not over a prime field.

Vincent

Hello,

Indeed there is The problem comes from the fact that your matrix does not have full rank (indeed it has rank 3 and 7 rows). If you use a bugfull rank matrix then you are done

sage: u C1 = C((0, 0, 0, 0, 0, 0, 0))
LinearCode(G)
sage: v C2 = C((1, 0, 0, a + 1, 0, 1, 0))
LinearCode(G[:3])
sage: u in C and v in C
C1 == C2
True
sage: C1.minimum_distance()
5
sage: C2.minimum_distance()
3

And I opened a trac ticket for that problem. It will be modified in the hamming weight of v = v-u is 3... Actually there are two algorithms in Sage and both of them failnext stable release. Thanks for your report!

sage: LinearCode(G).minimum_distance(algorithm="guava")
5
sage: LinearCode(G).minimum_distance(algorithm="gap")
5

One possible reason is that it is If you want to contribute to Sage, do not over hesitate to open a prime field.trac account and participate in the resolution of this problem.

Vincent

Hello,

The problem comes from the fact that your matrix does not have full rank (indeed it has rank 3 and 7 rows). If you use a full rank matrix then you are done

sage: C1 = LinearCode(G)
sage: C2 = LinearCode(G[:3])
sage: C1 == C2
True
sage: C1.minimum_distance()
5
sage: C2.minimum_distance()
3

I opened a the trac ticketticket #17452 for that problem. It will be modified in the next stable release. Thanks for your report!

If you want to contribute to Sage, do not hesitate to open a trac account and participate in the resolution of this problem.

Vincent