  Consider the identification (ID) via channels problem, where a receiver wants
to decide whether the transmitted identifier is its identifier, rather than
decoding the identifier. This model allows to transmit identifiers whose size
scales doubly-exponentially in the blocklength, unlike common transmission (or
channel) codes whose size scales exponentially. It suffices to use binary
constant-weight codes (CWCs) to achieve the ID capacity. By relating the
parameters of a binary CWC to the minimum distance of a code and using
higher-order correlation moments, two upper bounds on the binary CWC size are
proposed. These bounds are shown to be upper bounds also on the identifier
sizes for ID codes constructed by using binary CWCs. We propose two code
constructions based on optical orthogonal codes, which are used in optical
multiple access schemes, have constant-weight codewords, and satisfy cyclic
cross-correlation and auto-correlation constraints. These constructions are
modified and concatenated with outer Reed-Solomon codes to propose new binary
CWCs optimal for ID. Improvements to the finite-parameter performance of both
our and existing code constructions are shown by using outer codes with larger
minimum distance vs. blocklength ratios. We also illustrate ID performance
regimes for which our ID code constructions perform significantly better than
existing constructions.
