Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Power Decoding Reed--Solomon Codes Up to the Johnson Radius   Power decoding, or "decoding using virtual interleaving" is a technique for
decoding Reed--Solomon codes up to the Sudan radius. Since the method's
inception, it has been an open question if it is possible to use this approach
to decode up to the Johnson radius -- the decoding radius of the
Guruswami--Sudan algorithm. In this paper we show that this can be done by
incorporating a notion of multiplicities. As the original Power decoding, the
proposed algorithm is a one-pass algorithm: decoding follows immediately from
solving a shift-register type equation, which we show can be done in
quasi-linear time. It is a "partial bounded-distance decoding algorithm" since
it will fail to return a codeword for a few error patterns within its decoding
radius; we investigate its failure behaviour theoretically as well as give
simulation results.
  This is an extended version where we also show how the method can be made
faster using the re-encoding technique or a syndrome formulation.

13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom