[Next] [Prev] [Right] [Left] [Up] [Index] [Root]
Bounds

Bounds

Magma supplies various functions for computing lower and upper bounds for parameters associated with codes.

Subsections

Upper Bounds on the Cardinality of a Largest Code

EliasBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
Return the Elias upper bound of the cardinality of a largest code of length n and minimum distance d over the field K.
GriesmerBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
Return the Griesmer upper bound of the cardinality of a largest code of length n and minimum distance d over the field K.
JohnsonBound(n, d) : RngIntElt, RngIntElt -> RngIntElt
Return the Johnson upper bound of the cardinality of a largest binary code of length n and minimum distance d.
LevenshteinBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
Return the LevenshteinBound upper bound of the cardinality of a largest code of length n and minimum distance d over the field K.
PlotkinBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
Return the Plotkin upper bound of the cardinality of a largest code of length n and minimum distance d over the field K.
SingletonBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
Return the Singleton upper bound of the cardinality of a largest code of length n and minimum distance d over the field K.

Lower Bounds on the Cardinality of a Largest Code

GilbertVarshamovBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
Return the Gilbert-Varshamov lower bound of the cardinality of a largest code of length n and minimum distance d over the field K.
VanLintBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
Return the Van Lint lower bound of the cardinality of a largest code of length n and minimum distance d over the field K.

Upper Asymptotic Bounds on the Information Rate

EliasAsymptoticBound(K, delta) : FldFin, FldPrElt -> FldPrElt
Return the Elias asymptotic upper bound of the information rate for delta in [0, 1] over the field K.
McElieceEtAlAsymptoticBound(delta) : FldPrElt -> FldPrElt
Return the McEliece-Rodemich-Rumsey-Welch asymptotic upper bound of the binary information rate for delta in [0, 1].
PlotkinAsymptoticBound(K, delta) : FldFin, FldPrElt -> FldPrElt
Return the Plotkin asymptotic upper bound of the information rate for delta in [0, 1] over the field K.
SingletonAsymptoticBound(delta) : FldPrElt -> FldPrElt
Return the Singleton asymptotic upper bound of the information rate for delta in [0, 1] over any finite field.

Other Bounds

BKABdsInfoRate(K, delta) : FldFin, FldPrElt -> FldPrElt, FldPrElt
Return the best known asymptotic lower and upper bound of the information rate for delta in [0, 1] over the field K.
BKBdsCardLargestCode(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt, RngIntElt
Return the best known lower bound and upper bound for the cardinality of a largest code of length n and minimum distance d over the field K.
BKBdsCardLargestLinearCode(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt, RngIntElt
Return the best known lower bound and upper bound for the cardinality of a largest linear code of length n and minimum distance d over the field K.
BKBdsMaxMinimumWeight(K, n, k) : FldFin, RngIntElt, RngIntElt -> RngIntElt, RngIntElt
Return the best known lower bound and upper bound to the maximal minimum weight of a linear code of length n and dimension k over the field K.
[Next] [Prev] [Right] [Left] [Up] [Index] [Root]