Antichain Codes

Introduction A binary vector x is identiøed with its support, the set of its non-zero coordinate positions. Logarithms are binary. We consider binary linear codes C[n; k; d] with weight hierarchy fd = d 1 ; : : : ; d k = ng, where d i is the minimum support size of a i-th dimensional subcode of C. Asymptotically, we deal with normalized quantities, namely C[n; nR; nffi]; fffi 1 = ffi; : : : ; ffi nR = 1g: In the wire-tap channel (see [8]), the dual of C is used in a coset-coding scheme: the interception by an enemy of d i well chosen binary digits leaks i information bits about the system. If<F54.3