Towards a Gröbner-free approach to coding
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Publication:6146596
DOI10.1007/s10623-023-01302-9OpenAlexW4387616280MaRDI QIDQ6146596
Ferdinando Mora, Michela Ceria
Publication date: 15 January 2024
Published in: Designs, Codes and Cryptography (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10623-023-01302-9
Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Cyclic codes (94B15) Decoding (94B35) Combinatorial aspects of commutative algebra (05E40)
Cites Work
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- Correcting errors and erasures via the syndrome variety
- HELP: a sparse error locator polynomial for BCH codes
- Bar code: a visual representation for finite sets of terms and its applications
- The big mother of all dualities. 2: Macaulay bases
- Matrix multiplication via arithmetic progressions
- On the decoding of cyclic codes using Gröbner bases
- De nugis Groebnerialium. II: Applying Macaulay's trick in order to easily write a Gröbner basis
- Ideal basis and primary decompositions: case of two variables
- Multivariate interpolation and standard bases for Macaulay modules
- The Chen-Reed-Helleseth-Truong decoding algorithm and the Gianni-Kalkbrenner Gröbner shape theorem
- A remark on a remark by Macaulay or enhancing Lazard structural theorem
- From algebraic sets to monomial linear bases by means of combinatorial algorithms
- Bar code for monomial ideals
- Degröbnerization: a political manifesto
- Fast Gröbner basis computation and polynomial reduction for generic bivariate ideals
- Gröbner bases of ideals defined by functionals with an application to ideals of projective points
- The lex game and some applications
- Vector space bases associated to vanishing ideals of points
- Finding BCH error locator polynomials in one step
- Fundamentals of Error-Correcting Codes
- Use of Grobner bases to decode binary cyclic codes up to the true minimum distance
- General principles for the algebraic decoding of cyclic codes
- On the Shape of the General Error Locator Polynomial for Cyclic Codes
- Solving systems of algebraic equations by using gröbner bases
- Properties of Gröbner bases under specializations
- Invited Talk: Decoding Cyclic Codes: The Cooper Philosophy
- Combinatorial algorithms for the interpolation of polynomials in dimension \(\geq 2\)
- Applications of bar code to involutive divisions and a ``greedy algorithm for complete sets
