Published on December 16, 2016 by Microsoft Research
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The systematic normal form of lattices is a new echelon form of lattices in which the entries obey a certain co-primality condition. These lattices can be used to approximate efficiently any lattice, and hence are as hard to solve as any lattice. We show that this special structure gives rise to several interesting mathematical properties, connecting their primal and dual lattices, which in turn offer certain natural quantum and classical computational primitives which are otherwise not known to exist. We present these primitives as a possible handle to make progress to solve computationally-hard lattice problems.

See more on this video at www.microsoft.com/en-us/research/video/systematic-normal-form-lattices-algorithmic-applications-joint-work-peter-shor-lior-eldar/

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5 Comments on "The systematic normal form of lattices, and their algorithmic applications."

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Bob Looter
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Bob Looter
11 months 2 days ago

thanks, will you answer my questions. ? BDD uses latice method but in ' error ' correction you can not use polynomial computation since it can make error's on it's own. This method of BDD is owning as heritage of ( new proximity in polynomial vectoring ) it can not use BDD as a stand alone function.

Bob Looter
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Bob Looter
11 months 2 days ago

what method do you use in error correction ?

Bob Looter
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Bob Looter
11 months 2 days ago

Fantastic , i understand this for it can be adapted to new as well old. Good presentation..

Bob Looter
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Bob Looter
11 months 2 days ago

Bill Gates, give this guy more room and staff for he will make things right.

Bob Looter
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Bob Looter
11 months 2 days ago

Fantastic, this is a good polynomial implementation and very adaptive way to implement a new ' abstract ' value. Keep going on this for it is where it can be adapted to any systems,Conventional side we been missing this since the start.

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