Optimal linear identifying codes

Identifying codes can be used to locate malfunctioning processors. We say that a code C of length n is a linear (1,<=l)identifying code if it is a subspace of F/sub 2//sup n/ and for all X,Y/spl sube/F/sub 2//sup n/ such that |X|, |Y|<=l and X(not equal)Y, we have /spl cup//sub x/spl isin/X/(B(x)/spl cap/C)(not equal)/spl cup/y/spl isin/Y(B(y)/spl cap/C). Strongly (1,<=l)-identifying codes are a variant of identifying codes. We determine the cardinalities of optimal linear (1,<=l)-identifying and strongly (1,<=l)identifying codes in Hamming spaces of any dimension for locating any at most l malfunctioning processors.