|
Along with the database of best known quantum codes in the previous
section, there is also a database of best known upper and lower
bounds on the maximal possible minimum weights of quantum codes.
The upper bounds are not currently known with much accuracy,
while the lower bounds match the minimum weights
of the best known quantum codes database.
Return the best known lower bound on the maximal minimum distance
of [[n, k]] quantum codes over F.
The bounds are currently available for binary quantum codes
(which corresponds to F = GF(4)) up to length 35.
Return the best known upper bound on the minimum distance
of [[n, k]] quantum codes over F.
The bounds are currently available for binary quantum codes
(which corresponds to F = GF(4)) up to length 35.
The best known lower bound on the minimum weight will always
correspond to the best known quantum code from the Magma database.
In this example the first code is in fact optimal, while
the second one does not meet the upper bound, and so there
is a theoretical possibility of an improvement.
> F<w> := GF(4);
> Q1 := QECC(F, 20, 10);
> Q1:Minimal;
[[20, 10, 4]] Quantum code over GF(2^2)
> QECCLowerBound(F, 20, 10);
4
> QECCUpperBound(F, 20, 10);
4
>
> Q2 := QECC(F, 25, 13);
> Q2:Minimal;
[[25, 13, 4]] Quantum code over GF(2^2)
> QECCLowerBound(F, 25, 13);
4
> QECCUpperBound(F, 25, 13);
5
[Next][Prev] [Right] [Left] [Up] [Index] [Root]
|