This section describes the functions that calculate estimates for upper bounds on the size and minimum distance of codes. Several algorithms are known to compute a largest number of words a code can have with given length and minimum distance. It is important however to understand that in some cases the true upper bound is unknown. A code which has a size equal to the calculated upper bound may not have been found. However, codes that have a larger size do not exist.
A second way to obtain bounds is a table. In GUAVA, an extensive table is implemented for linear codes over GF(2), GF(3) and GF(4). It contains bounds on the minimum distance for given word length and dimension. For binary codes, it contains entries for word length less than or equal to 257. For codes over GF(3) and GF(4), it contains entries for word length less than or equal to 130.
The next sections describe functions that compute specific upper bounds on the code size (see UpperBoundSingleton, UpperBoundHamming, UpperBoundJohnson, UpperBoundPlotkin, UpperBoundElias and UpperBoundGriesmer).
The next section describes a function that computes GUAVA's best upper bound on the code size (see UpperBound).
The next sections describe two function that compute a lower and upper bound on the minimum distance of a code (see LowerBoundMinimumDistance and UpperBoundMinimumDistance).
The last section describes a function that returns a lower and upper bound on the minimum distance with given parameters and a description how the bounds were obtained (see BoundsMinimumDistance).
GAP 3.4.4