65.150 LowerBoundCoveringRadiusSphereCovering

LowerBoundCoveringRadiusSphereCovering( n, M [, F ], false )

LowerBoundCoveringRadiusSphereCovering( n, r [, F ] [, true ] )

If the last argument of LowerBoundCoveringRadiusSphereCovering is false, then it returns a lower bound for the covering radius of a code of size M and length n. Otherwise, it returns a lower bound for the size of a code of length n and covering radius r.

F is the field over which the code is defined. If F is omitted, it is assumed that the code is over GF(2).

The bound is computed according to the sphere covering bound:

M V_q(n,r) geq q^n

where V_q(n,r) is the size of a sphere of radius r in GF(q)^n.

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