On the decoding of binary cyclic codes with the Newton identities

DOI10.1016/j.jsc.2008.02.006zbMath1174.94023OpenAlexW2165211986MaRDI QIDQ733502

Jean-Charles Faugère, Magali Bardet, Daniel Augot

Publication date: 16 October 2009

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://hal.inria.fr/inria-00509219/file/gbdecode-revised.pdf

zbMATH Keywords

Gröbner basiselimination theorycyclic codesquadratic residue codes\(F4\) algorithm

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Cyclic codes (94B15)

Related Items (4)

Matrix-product structure of repeated-root cyclic codes over finite fields ⋮ Improved decoding of affine-variety codes ⋮ A Variant of the F4 Algorithm ⋮ Degröbnerization: a political manifesto

Uses Software

• FGb
• McEliece

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Correcting errors and erasures via the syndrome variety
• A new efficient algorithm for computing Gröbner bases \((F_4)\)
• On the decoding of cyclic codes using Gröbner bases
• The Chen-Reed-Helleseth-Truong decoding algorithm and the Gianni-Kalkbrenner Gröbner shape theorem
• Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
• New linear codes derived from binary cyclic codes of length 151
• Finding BCH error locator polynomials in one step
• Algebraic decoding of the (32, 16, 8) quadratic residue code
• General Error Locator Polynomials for Binary Cyclic Codes With <formula formulatype="inline"><tex>$t \le 2$</tex></formula> and <formula formulatype="inline"> <tex>$n &lt; 63$</tex></formula>
• Studying the locator polynomials of minimum weight codewords of BCH codes
• The algebraic decoding of the (41, 21, 9) quadratic residue code
• Decoding the (73, 37, 13) quadratic residue code
• Use of Grobner bases to decode binary cyclic codes up to the true minimum distance
• General principles for the algebraic decoding of cyclic codes
• A new algorithm for finding minimum-weight words in a linear code: application to McEliece's cryptosystem and to narrow-sense BCH codes of length 511
• Decoding the (47,24,11) quadratic residue code
• Using Algebraic Geometry
• Fast algorithms for decoding the (23, 12) binary Golay code with four-error-correcting capability
• Cyclic decoding procedures for Bose- Chaudhuri-Hocquenghem codes
• Solving systems of algebraic equations by using gröbner bases
• Properties of Gröbner bases under specializations

This page was built for publication: On the decoding of binary cyclic codes with the Newton identities