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» Linear Network Codes and Systems of Polynomial Equations

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TIT
2008

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Linear Network Codes and Systems of Polynomial Equations

13 years 4 months ago

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If and are nonnegative integers and F is a field, then a polynomial collection {p1, . . . , p} Z[1, . . . , ] is said to be solvable over F if there exist 1, . . . , F such t...

Randall Dougherty, Christopher F. Freiling, Kennet...

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CORR
2008
Springer

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A Simple Algebraic Formulation for the Scalar Linear Network Coding Problem

13 years 5 months ago

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In this work, we derive an algebraic formulation for the scalar linear network coding problem as an alternative to the one presented by Koetter et al in [1]. Using an equivalence b...

Abhay T. Subramanian, Andrew Thangaraj

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FOCS
2002
IEEE

129views Theoretical Computer Science» more FOCS 2002»

Linear Diophantine Equations over Polynomials and Soft Decoding of Reed-Solomon Codes

13 years 9 months ago

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Abstract—This paper generalizes the classical Knuth–Schönhage algorithm computing the greatest common divisor (gcd) of two polynomials for solving arbitrary linear Diophantine...

Michael Alekhnovich

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JSC
2010

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Linear complete differential resultants and the implicitization of linear DPPEs

12 years 11 months ago

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The linear complete differential resultant of a finite set of linear ordinary differential polynomials is defined. We study the computation by linear complete differential resulta...

Sonia L. Rueda, J. Rafael Sendra

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DAM
2006

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A strongly polynomial algorithm for solving two-sided linear systems in max-algebra

13 years 4 months ago