
Decodable quantum LDPC codes beyond the √(n) distance barrier using high dimensional expanders
Constructing quantum LDPC codes with a minimum distance that grows faste...
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Locally recoverable Jaffine variety codes
We prove that subfieldsubcodes over finite fields F_q of some Jaffine ...
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Decoding of Lifted AffineInvariant Codes
Lifted ReedSolomon codes, a subclass of lifted affineinvariant codes, ...
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Projective toric codes
Any integral convex polytope P in R^N provides a Ndimensional toric var...
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A Study of the Separating Property in ReedSolomon Codes by Bounding the Minimum Distance
According to their strength, the tracing properties of a code can be cat...
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Squares of Matrixproduct Codes
The componentwise or Schur product C*C' of two linear error correcting ...
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From primary to dual affine variety codes over the Klein quartic
In [17] a novel method was established to estimate the minimum distance ...
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High dimensional affine codes whose square has a designed minimum distance
Given a linear code C, its square code C^(2) is the span of all componentwise products of two elements of C. Motivated by applications in multiparty computation, our purpose with this work is to answer the following question: which families of affine variety codes have simultaneously high dimension k(C) and high minimum distance of C^(2), d(C^(2))? More precisely, given a designed minimum distance d we compute an affine variety code C such that d(C^(2))≥ d and that the dimension of C is high. The best construction that we propose comes from hyperbolic codes when d> q and from weighted ReedMuller codes otherwise.
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