Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High dimensional expansion implies amplified local testability   In this work we show that high dimensional expansion implies locally testable
code. Specifically, we define a notion that we call
high-dimensional-expanding-system (HDE-system). This is a set system defined by
incidence relations with certain high dimensional expansion relations between
its sets. We say that a linear code is modelled over HDE-system, if the
collection of linear constraints that the code satisfies could by described via
the HDE-system. We show that a code that can be modelled over HDE-system is
locally testable.
  This implies that high dimensional expansion phenomenon solely implies local
testability of codes. Prior work had to rely to local notions of local
testability to get some global forms of testability (e.g. co-systolic expansion
from local one, global agreement from local one), while our work infers global
testability directly from high dimensional expansion without relying on some
local form of testability.
  The local testability result that we obtain from HDE-systems is, in fact,
stronger than standard one, and we term it amplified local testability.
  We further show that most of the well studied locally testable codes as
Reed-Muller codes and more generally affine invariant codes with single-orbit
property fall into our framework. Namely, it is possible to show that they are
modelled over an HDE-system, and hence the family of all p-ary affine invariant
codes is amplified locally testable. This yields the strongest known testing
results for affine invariant codes with single orbit, strengthening the work of
Kaufman and Sudan.

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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat