On the Dimension of Algebraic-Geometric Trace Codes
We study trace codes induced from codes defined by an algebraic curve X. We determine conditions on X which admit a formula for the dimension of such a trace code. Central to our work are several dimension reducing methods for the underlying functions spaces associated to X.
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| Format: | Article |
| Language: | English |
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MDPI AG
2016-05-01
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| Series: | Mathematics |
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| Online Access: | http://www.mdpi.com/2227-7390/4/2/32 |
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doaj-31e8c12b451746dda6c1913ff0c723052020-11-25T00:14:02ZengMDPI AGMathematics2227-73902016-05-01423210.3390/math4020032math4020032On the Dimension of Algebraic-Geometric Trace CodesPhong Le0Sunil Chetty1Department of Mathematics and Computer Science, Goucher College, Baltimore, MD 21204, USADepartment of Mathematics, College of Saint Benedict and Saint John’s University, Collegeville, MN 56321, USAWe study trace codes induced from codes defined by an algebraic curve X. We determine conditions on X which admit a formula for the dimension of such a trace code. Central to our work are several dimension reducing methods for the underlying functions spaces associated to X.http://www.mdpi.com/2227-7390/4/2/32error correcting codestrace codesexponential sumsnumber theory11T71 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Phong Le Sunil Chetty |
| spellingShingle |
Phong Le Sunil Chetty On the Dimension of Algebraic-Geometric Trace Codes Mathematics error correcting codes trace codes exponential sums number theory 11T71 |
| author_facet |
Phong Le Sunil Chetty |
| author_sort |
Phong Le |
| title |
On the Dimension of Algebraic-Geometric Trace Codes |
| title_short |
On the Dimension of Algebraic-Geometric Trace Codes |
| title_full |
On the Dimension of Algebraic-Geometric Trace Codes |
| title_fullStr |
On the Dimension of Algebraic-Geometric Trace Codes |
| title_full_unstemmed |
On the Dimension of Algebraic-Geometric Trace Codes |
| title_sort |
on the dimension of algebraic-geometric trace codes |
| publisher |
MDPI AG |
| series |
Mathematics |
| issn |
2227-7390 |
| publishDate |
2016-05-01 |
| description |
We study trace codes induced from codes defined by an algebraic curve X. We determine conditions on X which admit a formula for the dimension of such a trace code. Central to our work are several dimension reducing methods for the underlying functions spaces associated to X. |
| topic |
error correcting codes trace codes exponential sums number theory 11T71 |
| url |
http://www.mdpi.com/2227-7390/4/2/32 |
| work_keys_str_mv |
AT phongle onthedimensionofalgebraicgeometrictracecodes AT sunilchetty onthedimensionofalgebraicgeometrictracecodes |
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1725391808926580736 |