On Constant-Weight Binary B2-Sequences

Jin Sima, Yun-Han Li, Ilan Shomorony, Olgica Milenkovic

Abstract: Motivated by applications in polymer-based data storage we introduced the new problem of characterizing the code rate and designing constant-weight binary B<inf>2</inf>-sequences. Binary B<inf>2</inf>-sequences are collections of binary strings of length nwith the property that the real-valued sums of all distinct pairs of strings are distinct. In addition to this defining property, constant-weight binary B<inf>2</inf>-sequences also satisfy the constraint that each string has a fixed, relatively small weight ωthat scales linearly with n. The constant-weight constraint ensures low-cost synthesis and uniform processing of the data readout via tandem mass spectrometers. Our main results include upper bounds on the size of the codes formulated as entropy-optimization problems and constructive lower bounds based on Sidon sequences.