65.153 LowerBoundCoveringRadiusCountingExcess

LowerBoundCoveringRadiusCountingExcess( n, M, false )

LowerBoundCoveringRadiusCountingExcess( n, r [, true ] )

If the last argument of LowerBoundCoveringRadiusCountingExcess 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 left( rho V_2(n,r) + varepsilon V_2(n,r-1) right) geq (rho + varepsilon) 2^n,

where varepsilon = (r+1) leftlceilfracn+1r+1rightrceil - (n+1)

and rho = left{ beginarrayll n-3+frac2n & mbox if r = 2
n-r-1 & mbox if r geq 3 endarray right.

Previous Up Top Next
Index