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,/spl les/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|/spl les/l and X/spl ne/Y, we have /spl cup//sub x/spl isin/X/(B(x)/spl cap/C)/spl ne//spl cup/y/spl isin/Y(B(y)/spl cap/C). Strongly (1,/spl les/l)-identifying codes are a variant of identifying codes. We determine the cardinalities of optimal linear (1,/spl les/l)-identifying and strongly (1,/spl les/l)-identifying codes in Hamming spaces of any dimension for locating any at most l malfunctioning processors.