Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient Majority-Logic Decoding of Short-Length Reed--Muller Codes at
  Information Positions   Short-length Reed--Muller codes under majority-logic decoding are of
particular importance for efficient hardware implementations in real-time and
embedded systems. This paper significantly improves Chen's two-step
majority-logic decoding method for binary Reed--Muller codes $\text{RM}(r,m)$,
$r \leq m/2$, if --- systematic encoding assumed --- only errors at information
positions are to be corrected. Some general results on the minimal number of
majority gates are presented that are particularly good for short codes.
Specifically, with its importance in applications as a 3-error-correcting,
self-dual code, the smallest non-trivial example, $\text{RM}(2,5)$ of dimension
16 and length 32, is investigated in detail. Further, the decoding complexity
of our procedure is compared with that of Chen's decoding algorithm for various
Reed--Muller codes up to length $2^{10}$.

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The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph