Testing algebraic geometric codes |
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Authors: | Hao Chen |
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Institution: | CHEN Hao Software Engineering Institute,East China Normal University,Shanghai 200062,China |
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Abstract: | Property testing was initially studied from various motivations in 1990’s. A code C ⊂ GF(r)
n
is locally testable if there is a randomized algorithm which can distinguish with high possibility the codewords from a vector
essentially far from the code by only accessing a very small (typically constant) number of the vector’s coordinates. The
problem of testing codes was firstly studied by Blum, Luby and Rubinfeld and closely related to probabilistically checkable
proofs (PCPs). How to characterize locally testable codes is a complex and challenge problem. The local tests have been studied
for Reed-Solomon (RS), Reed-Muller (RM), cyclic, dual of BCH and the trace subcode of algebraicgeometric codes. In this paper
we give testers for algebraic geometric codes with linear parameters (as functions of dimensions). We also give a moderate
condition under which the family of algebraic geometric codes cannot be locally testable. |
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Keywords: | number theory of finite field property testing algebraic geometric codes |
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