Efficient decoding of interleaved subspace and Gabidulin codes beyond their unique decoding radius using Gröbner bases

Hannes Bartz;  ; Antonia Wachter-Zeh;

doi:10.3934/amc.2018046

Efficient decoding of interleaved subspace and Gabidulin codes beyond their unique decoding radius using Gröbner bases

Advances in Mathematics of Communications ◽

10.3934/amc.2018046 ◽

2018 ◽

Vol 12 (4) ◽

pp. 773-804 ◽

Cited By ~ 3

Author(s):

Hannes Bartz ◽

◽

Antonia Wachter-Zeh ◽

Keyword(s):

Gröbner Bases ◽

Grobner Bases ◽

Gabidulin Codes ◽

Efficient Decoding

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Efficient decoding of (binary) cyclic codes above the correction capacity of the code using grobner bases

IEEE International Symposium on Information Theory, 2003. Proceedings. ◽

10.1109/isit.2003.1228378 ◽

2003 ◽

Cited By ~ 7

Author(s):

D. Augot ◽

M. Bardet ◽

J.-C. Faugere

Keyword(s):

Cyclic Codes ◽

Gröbner Bases ◽

Grobner Bases ◽

Efficient Decoding

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A Reachability Test for Systems over Polynomial Rings using Gröbner Bases

1993 American Control Conference ◽

10.23919/acc.1993.4792842 ◽

1993 ◽

Cited By ~ 1

Author(s):

L.C.G.J.M. Habets

Keyword(s):

Gröbner Bases ◽

Grobner Bases ◽

Polynomial Rings

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The 50th Anniversary of Gröbner Bases

10.2969/aspm/07710000 ◽

2018 ◽

Keyword(s):

Gröbner Bases ◽

50Th Anniversary ◽

Grobner Bases

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Gröbner bases for operads

Duke Mathematical Journal ◽

10.1215/00127094-2010-026 ◽

2010 ◽

Vol 153 (2) ◽

pp. 363-396 ◽

Cited By ~ 55

Author(s):

Vladimir Dotsenko ◽

Anton Khoroshkin

Keyword(s):

Gröbner Bases ◽

Grobner Bases

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Signature-based algorithms for Gröbner bases over tate algebras

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation ◽

10.1145/3373207.3404035 ◽

2020 ◽

Author(s):

Xavier Caruso ◽

Tristan Vaccon ◽

Thibaut Verron

Keyword(s):

Gröbner Bases ◽

Grobner Bases

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Computation of free non-commutative gröbner bases over Z with Singular:Letterplace

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation ◽

10.1145/3373207.3404052 ◽

2020 ◽

Cited By ~ 1

Author(s):

Viktor Levandovskyy ◽

Tobias Metzlaff ◽

Karim Abou Zeid

Keyword(s):

Gröbner Bases ◽

Grobner Bases

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Some theoretical problems when solving systems of polynomial equations using Gröbner bases

ACM SIGSAM Bulletin ◽

10.1145/122520.122523 ◽

1991 ◽

Vol 25 (2) ◽

pp. 24-27 ◽

Cited By ~ 1

Author(s):

S. Alasdair Buchanan

Keyword(s):

Gröbner Bases ◽

Grobner Bases ◽

Polynomial Equations ◽

Systems Of Polynomial Equations

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Partial Gröbner Bases for Multiobjective Integer Linear Optimization

SIAM Journal on Discrete Mathematics ◽

10.1137/070698051 ◽

2009 ◽

Vol 23 (2) ◽

pp. 571-595 ◽

Cited By ~ 8

Author(s):

Víctor Blanco ◽

Justo Puerto

Keyword(s):

Linear Optimization ◽

Gröbner Bases ◽

Grobner Bases ◽

Integer Linear Optimization

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Gröbner bases over fields with valuations

Mathematics of Computation ◽

10.1090/mcom/3321 ◽

2018 ◽

Vol 88 (315) ◽

pp. 467-483 ◽

Cited By ~ 7

Author(s):

Andrew J. Chan ◽

Diane Maclagan

Keyword(s):

Gröbner Bases ◽

Grobner Bases

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Using noncommutative Gröbner bases in solving partially prescribed matrix inverse completion problems

Linear Algebra and its Applications ◽

10.1016/s0024-3795(01)00382-2 ◽

2001 ◽

Vol 338 (1-3) ◽

pp. 171-199 ◽

Cited By ~ 1

Author(s):

F. Dell Kronewitter

Keyword(s):

Gröbner Bases ◽

Grobner Bases ◽

Matrix Inverse ◽

Completion Problems

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