Skew Reed-Muller codes

DOI10.1090/conm/727/14628zbMath1422.94037OpenAlexW2938252573MaRDI QIDQ5239119

Felix Ulmer, Willi Geiselmann

Publication date: 22 October 2019

Published in: Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/conm/727/14628

zbMATH Keywords

skew polynomial ringsGröbner basislinear codes

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Computational aspects of associative rings (general theory) (16Z05)

Related Items

Classification of multivariate skew polynomial rings over finite fields via affine transformations of variables, Fast Kötter-Nielsen-Høholdt interpolation over skew polynomial rings and its application in coding theory, Evaluation of iterated Ore polynomials and skew Reed-Muller codes, On skew partial derivatives and a Hermite-type interpolation problem, Theory and applications of linearized multivariate skew polynomials, Rank-Metric Codes Over Arbitrary Galois Extensions and Rank Analogues of Reed--Muller Codes

Uses Software

• GBGR.mpl

Cites Work

• Unnamed Item
• A signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings.
• Theory of codes with maximum rank distance
• Vandermonde and Wronskian matrices over division rings
• Linear codes using skew polynomials with automorphisms and derivations
• Ore polynomial rings in one variable in computer algebra.
• APPLYING BUCHBERGER'S CRITERIA FOR COMPUTING GRÖBNER BASES OVER FINITE-CHAIN RINGS