Weight structure of binary codes and the performance of blind search algorithms

Algebraic block codes are vector linear subspaces defined over a finite field. The original problem of the block codes applied was that of protecting information against error during transmission over communication channels. However, combinatorial coding theory is an independent area of investigations. Algebraic codes own fertile geometric properties. Packing and covering radii are two important parameters of an algebraic code. In the author's previous paper (1997), two inequalities relating these parameters with thoroughness and sparsity of a blind search algorithm were established. In this paper we present a closed expression for the thoroughness of a random blind search algorithm in two cases: baseline random search and random blind search guided by an algebraic code. We interpret the "worst case " random search approach as a starting point for future research.