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An Approach to the Bases of Riemann-Roch Spaces (Journal Article)

By:

Hu, Chuangqiang

Contributor(s):

Yang, Shudi

Material type: Text

TextSeries: Indian Journal of Pure and Applied Mathematics ; , Volume 54: Number 4, December 2023Publication details: New Delhi , 2023Description: 1239-1248pISSN:

0019-5588

Subject(s):

Riemann-Roch space| Function field| AG code

Online resources:

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Contents:

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Summary: Abstract: For applications in algebraic geometric codes, it is extremely useful to give an explicit description of the bases of Riemann-Roch spaces associated to divisors on function fields over finite fields. We demonstrate a general approach to construct such a monomial basis for the related Riemann-Roch space. More precisely we present a criterion for finding an explicit basis for the Riemann-Roch space of a three-point divisor. Furthermore, we improve an upper bound for the genus of the related function field. Some examples are also given to illustrate our general approach.

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Item type	Current library	Call number	Status	Date due	Barcode
Periodicals	RIE BPL Library		Not for loan

***______{For Hard Copy, Please visit Library.}________***

Abstract: For applications in algebraic geometric codes, it is extremely useful to give an explicit description of the bases of Riemann-Roch spaces associated to divisors on function fields over finite fields. We demonstrate a general approach to construct such a monomial basis for the related Riemann-Roch space. More precisely we present a criterion for finding an explicit basis for the Riemann-Roch space of a three-point divisor. Furthermore, we improve an upper bound for the genus of the related function field. Some examples are also given to illustrate our general approach.

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An Approach to the Bases of Riemann-Roch Spaces (Journal Article)

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