Abstract
Let us denote by ( n,k,d )-code, a binary linear code with code length n k information symbols and the minimum distance d . It is well known that the problem of obtaining a binary linear code whose code length n is minimum among ( n,k,d )-codes for given integers k and d , is equivalent to solve a linear programming whose solutions correspond to a minimum redundancy error-correcting code. In this paper it will be shown that for some given integers d , there exists no solution of the linear programming except a solution which is obtained using a flat in a finite projective geometry.
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