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On DNA codes from a family of chain rings
In this work, we focus on reversible cyclic codes which correspond to reversible DNA codes or reversible-complement DNA codes over a family of finite chain rings, in an effort to extend what was done by Yildiz and Siap in [20]. The ring family that we have considered are of size , and we match each ring element with a DNA -mer. We use the so-called -adic digit system to solve the reversibility problem and we characterize cyclic codes that correspond to reversible-complement DNA-codes. We then conclude our study with some examples
Mutually Uncorrelated Primers for DNA-Based Data Storage
We introduce the notion of weakly mutually uncorrelated (WMU) sequences,
motivated by applications in DNA-based data storage systems and for
synchronization of communication devices. WMU sequences are characterized by
the property that no sufficiently long suffix of one sequence is the prefix of
the same or another sequence. WMU sequences used for primer design in DNA-based
data storage systems are also required to be at large mutual Hamming distance
from each other, have balanced compositions of symbols, and avoid primer-dimer
byproducts. We derive bounds on the size of WMU and various constrained WMU
codes and present a number of constructions for balanced, error-correcting,
primer-dimer free WMU codes using Dyck paths, prefix-synchronized and cyclic
codes.Comment: 14 pages, 3 figures, 1 Table. arXiv admin note: text overlap with
arXiv:1601.0817
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