1,957 research outputs found
Design of Geometric Molecular Bonds
An example of a nonspecific molecular bond is the affinity of any positive
charge for any negative charge (like-unlike), or of nonpolar material for
itself when in aqueous solution (like-like). This contrasts specific bonds such
as the affinity of the DNA base A for T, but not for C, G, or another A. Recent
experimental breakthroughs in DNA nanotechnology demonstrate that a particular
nonspecific like-like bond ("blunt-end DNA stacking" that occurs between the
ends of any pair of DNA double-helices) can be used to create specific
"macrobonds" by careful geometric arrangement of many nonspecific blunt ends,
motivating the need for sets of macrobonds that are orthogonal: two macrobonds
not intended to bind should have relatively low binding strength, even when
misaligned.
To address this need, we introduce geometric orthogonal codes that abstractly
model the engineered DNA macrobonds as two-dimensional binary codewords. While
motivated by completely different applications, geometric orthogonal codes
share similar features to the optical orthogonal codes studied by Chung,
Salehi, and Wei. The main technical difference is the importance of 2D geometry
in defining codeword orthogonality.Comment: Accepted to appear in IEEE Transactions on Molecular, Biological, and
Multi-Scale Communication
n-Dimensional Optical Orthogonal Codes, Bounds and Optimal Constructions
We generalized to higher dimensions the notions of optical orthogonal codes.
We establish uper bounds on the capacity of general -dimensional OOCs, and
on specific types of ideal codes (codes with zero off-peak autocorrelation).
The bounds are based on the Johnson bound, and subsume many of the bounds that
are typically applied to codes of dimension three or less. We also present two
new constructions of ideal codes; one furnishes an infinite family of optimal
codes for each dimension , and another which provides an
asymptotically optimal family for each dimension . The constructions
presented are based on certain point-sets in finite projective spaces of
dimension over denoted .Comment: 13 pages. arXiv admin note: text overlap with arXiv:1702.0645
A General Upper Bound on the Size of Constant-Weight Conflict-Avoiding Codes
Conflict-avoiding codes are used in the multiple-access collision channel
without feedback. The number of codewords in a conflict-avoiding code is the
number of potential users that can be supported in the system. In this paper, a
new upper bound on the size of conflict-avoiding codes is proved. This upper
bound is general in the sense that it is applicable to all code lengths and all
Hamming weights. Several existing constructions for conflict-avoiding codes,
which are known to be optimal for Hamming weights equal to four and five, are
shown to be optimal for all Hamming weights in general.Comment: 10 pages, 1 figur
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