The problem of distributing a Cartesian product file on multiple disks to maximize the parallelism for partial match queries is addressed. C. Faloutsos et al. (1989) have proposed an allocation method for Cartesian product files on multiple disks by using linear error-correcting codes. The performance of the allocation method is analyzed. Some conditions under which the allocation method is strictly optimal for queries with a given number of unspecified attributes are presented. A necessary and sufficient condition for a linear code to give a strictly optimal allocation method is discussed. Formulas for the average response time on queries with w unspecified attributes, denoted T/sub w/, in terms of the weight distribution of the code or its dual code, and formulas for the average response time Ton all queries, are given. Several examples whose average response times T/sub w/ or T are close to theoretical lower bounds are presented.>