Modular Curves and Coding Theory: A Survey

被引：0
作者：
Li, Wen-Ching W. [1 ]
机构：
[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA
来源：
FINITE FIELDS: THEORY AND APPLICATIONS | 2010年 / 518卷
关键词：
algebraic geometry codes; modular curves; towers; Elkies' modularity conjecture; ASYMPTOTICALLY GOOD TOWERS; GLOBAL FUNCTION-FIELDS; TSFASMAN-VLADUT-ZINK; FINITE-FIELDS; DISTINGUISHED DIVISORS; GILBERT-VARSHAMOV; ALGEBRAIC CURVE; RATIONAL-POINTS; TAME TOWERS; CODES;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this survey article we explain the role modular curves played in the theory of error-correcting codes. The emphasis is on Elkies' modularity conjecture which predicts that all asymptotically optimal recursively defined towers of curves over finite fields with square cardinality arise from reductions of modular curves. The known examples support this conjecture. We discuss in detail key properties of the modular towers concerning this conjecture.
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页码：301 / 314
页数：14
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