65.151 LowerBoundCoveringRadiusVanWee1

LowerBoundCoveringRadiusVanWee1( n, M [, F ], false )

LowerBoundCoveringRadiusVanWee1( n, r [, F ] [, true ] )

If the last argument of LowerBoundCoveringRadiusVanWee1 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 Van Wee bound is an improvement of the sphere covering bound:

M left{ V_q(n,r) - fracbinomialnrlceilfracn-rr+1rceil left(leftlceilfracn+1r+1rightrceil - fracn+1r+1right) right} geq q^n

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