On Constant-Weight Binary B_2-Sequences

03/23/2023

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by   Jin Sima, et al.

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Motivated by applications in polymer-based data storage we introduced the new problem of characterizing the code rate and designing constant-weight binary B_2-sequences. Binary B_2-sequences are collections of binary strings of length n with 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_2-sequences also satisfy the constraint that each string has a fixed, relatively small weight ω that 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.