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Reports tagged with number fields:
TR01-002 | 6th December 2000
Venkatesan Guruswami

#### Constructions of Codes from Number Fields

We define number-theoretic error-correcting codes based on algebraic
number fields, thereby providing a generalization of Chinese Remainder
Codes akin to the generalization of Reed-Solomon codes to
Algebraic-geometric codes. Our construction is very similar to
(and in fact less general than) the one given by (Lenstra 1986), but
the ... more >>>

TR06-147 | 27th November 2006
Chris Peikert, Alon Rosen

#### Lattices that Admit Logarithmic Worst-Case to Average-Case Connection Factors

Revisions: 1

We demonstrate an \emph{average-case} problem which is as hard as
finding $\gamma(n)$-approximate shortest vectors in certain
$n$-dimensional lattices in the \emph{worst case}, where $\gamma(n) = O(\sqrt{\log n})$. The previously best known factor for any class
of lattices was $\gamma(n) = \tilde{O}(n)$.

To obtain our ... more >>>

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