1. An information conversion rule generating apparatus comprising: a memory; and a processor coupled to the memory, wherein the processor executes a process comprising: first generating a first conversion rule for converting a feature quantity vector into a binary string with a first bit length that is longer than a predetermined bit length; converting a first plurality of feature quantity vectors into a first plurality of binary strings by using the first conversion rule, first relationship information that include relationships of the first plurality of feature quantity vectors being stored in the memory; calculating distance fidelity values for each bit of a binary string converted by the first conversion rule, based on the first relationship information and bit values of the first plurality of binary strings; and second generating a conversion rule for converting a feature quantity vector into a binary string with the predetermined bit length, based on the first conversion rule and the calculated distance fidelity values.