Algebraic geometric codes with applications

doi:10.1007/s11464-007-0001-x

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Front. Math. China ›› 2007, Vol. 2 ›› Issue (1) : 1-11. DOI: 10.1007/s11464-007-0001-x

Algebraic geometric codes with applications

CHEN Hao

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Abstract

The theory of linear error-correcting codes from algebraic geometric curves (algebraic geometric (AG) codes or geometric Goppa codes) has been well-developed since the work of Goppa and Tsfasman, Vladut, and Zink in 1981 1982. In this paper we introduce to readers some recent progress in algebraic geometric codes and their applications in quantum error-correcting codes, secure multi-party computation and the construction of good binary codes.