Algebraic Geometry Codes Export

@article{bhhv98, abstract = {The theory of error-correcting codes derived from curves in an algebraic geometry was initiated by the work of Goppa as generalizations of Bose-Chaudhuri-Hocquenghem (BCH), Reed–Solomon (RS), and Goppa codes. The development of the theory has received intense consideration since that time and the purpose of the paper is to review this work. Elements of the theory of algebraic curves, at a level sufficient to understand the code constructions and decoding algorithms, are introduced. Code constructions from particular classes of curves, including the Klein quartic, elliptic, and hyperelliptic curves, and Hermitian curves, are presented. Decoding algorithms for these classes of codes, and others, are considered. The construction of classes of asymptotically good codes using modular curves is also discussed.}, author = {Blake, I. and Heegard, C. and Hoeholdt, T. and Wei, V.}, citeulike-article-id = {106363}, citeulike-linkout-0 = {http://ieeexplore.ieee.org/iel4/18/15554/00720550.pdf}, journal = {IEEE Transactions on Information Theory}, keywords = {algebra, algebraicgeometry, codingtheory, finitefields, math}, posted-at = {2005-02-28 05:49:57}, priority = {4}, title = {Algebraic Geometry Codes}, url = {http://ieeexplore.ieee.org/iel4/18/15554/00720550.pdf}, year = {1998} }

TY - JOUR ID - bhhv98 L3 - citeulike-article-id:106363 N2 - The theory of error-correcting codes derived from curves in an algebraic geometry was initiated by the work of Goppa as generalizations of Bose-Chaudhuri-Hocquenghem (BCH), Reed–Solomon (RS), and Goppa codes. The development of the theory has received intense consideration since that time and the purpose of the paper is to review this work. Elements of the theory of algebraic curves, at a level sufficient to understand the code constructions and decoding algorithms, are introduced. Code constructions from particular classes of curves, including the Klein quartic, elliptic, and hyperelliptic curves, and Hermitian curves, are presented. Decoding algorithms for these classes of codes, and others, are considered. The construction of classes of asymptotically good codes using modular curves is also discussed. JF - IEEE Transactions on Information Theory TI - Algebraic Geometry Codes KW - algebra KW - algebraicgeometry KW - codingtheory KW - finitefields KW - math AU - Blake, I AU - Heegard, C AU - Hoeholdt, T AU - Wei, V PY - 1998/// UR - http://ieeexplore.ieee.org/iel4/18/15554/00720550.pdf ER -