CONSTRUCTING PARTIAL MDS CODES FROM REDUCIBLE ALGEBRAIC CURVES

被引：3

作者：

Bogart, Tristram ^{[1
]}

Horlemann-Trautmann, Anna-Lena ^{[2
]}

Karpuk, David ^{[3
]}

Neri, Alessandro ^{[4
]}

Velasco, Mauricio ^{[1
]}

机构：

[1] Univ los Andes, Dept Matemat, Bogota 11001000, Colombia

[2] Univ St Gallen, Sch Comp Sci, CH-9000 St Gallen, Switzerland

[3] F Secure Corp, Artificial Intelligence Ctr Excellence, PL 24, Helsinki 00181, Finland

[4] Tech Univ Munich, D-80333 Munich, Germany

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2021年 / 35卷 / 04期

基金：

瑞士国家科学基金会;

关键词：

algebraic geometric codes; reducible curves; locally repairable codes; PMDS codes; LOCALLY REPAIRABLE CODES; MAXIMALLY RECOVERABLE CODES;

D O I：

10.1137/20M1356658

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose reducible algebraic curves as a mechanism to construct partial maximum distance separable codes geometrically. We obtain new general existence results, new explicit constructions, and improved estimates on the smallest field sizes over which such codes can exist. Our results are obtained by combining ideas from projective algebraic geometry, combinatorics, and probability theory.

引用

页码：2946 / 2970

页数：25

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