36,924 research outputs found
The orbifold transform and its applications
We discuss the notion of the orbifold transform, and illustrate it on simple
examples. The basic properties of the transform are presented, including
transitivity and the exponential formula for symmetric products. The connection
with the theory of permutation orbifolds is addressed, and the general results
illustrated on the example of torus partition functions
Error-Correction in Flash Memories via Codes in the Ulam Metric
We consider rank modulation codes for flash memories that allow for handling
arbitrary charge-drop errors. Unlike classical rank modulation codes used for
correcting errors that manifest themselves as swaps of two adjacently ranked
elements, the proposed \emph{translocation rank codes} account for more general
forms of errors that arise in storage systems. Translocations represent a
natural extension of the notion of adjacent transpositions and as such may be
analyzed using related concepts in combinatorics and rank modulation coding.
Our results include derivation of the asymptotic capacity of translocation rank
codes, construction techniques for asymptotically good codes, as well as simple
decoding methods for one class of constructed codes. As part of our exposition,
we also highlight the close connections between the new code family and
permutations with short common subsequences, deletion and insertion
error-correcting codes for permutations, and permutation codes in the Hamming
distance
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