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Testing algebraic geometric codes

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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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Authors and Affiliations

  1. Software Engineering Institute, East China Normal University, Shanghai, 200062, China

    Hao Chen

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  1. Hao Chen
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Correspondence to Hao Chen.

Additional information

This work was partially supported by National Natural Science Foundation of China (Grant No. 10871068)

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Chen, H. Testing algebraic geometric codes. Sci. China Ser. A-Math. 52, 2171–2176 (2009). https://doi.org/10.1007/s11425-009-0141-4

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  • DOI: https://doi.org/10.1007/s11425-009-0141-4

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