On ConstantWeight Binary $B_2$Sequences
Abstract
Motivated by applications in polymerbased data storage we introduced the new problem of characterizing the code rate and designing constantweight binary $B_2$sequences. Binary $B_2$sequences are collections of binary strings of length $n$ with the property that the realvalued sums of all distinct pairs of strings are distinct. In addition to this defining property, constantweight binary $B_2$sequences also satisfy the constraint that each string has a fixed, relatively small weight $\omega$ that scales linearly with $n$. The constantweight constraint ensures lowcost 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 entropyoptimization problems and constructive lower bounds based on Sidon sequences.
 Publication:

arXiv eprints
 Pub Date:
 March 2023
 DOI:
 10.48550/arXiv.2303.12990
 arXiv:
 arXiv:2303.12990
 Bibcode:
 2023arXiv230312990S
 Keywords:

 Computer Science  Information Theory;
 Computer Science  Discrete Mathematics