65.152 LowerBoundCoveringRadiusVanWee2

LowerBoundCoveringRadiusVanWee2( n, M, false )

LowerBoundCoveringRadiusVanWee2( n, r [, true ] )

If the last argument of LowerBoundCoveringRadiusVanWee2 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.

This bound only works for binary codes.

It is based on the following inequality:

M fracleft( left( V_2(n,2) - frac12(r+2)(r-1) right) V_2(n,r) + varepsilon V_2(n,r-2) right) (V_2(n,2) - frac12(r+2)(r-1) + varepsilon) geq 2^n, where varepsilon = binomialr+22 leftlceil binomialn-r+12 / binomialr+22 rightrceil - binomialn-r+12.

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