Some remarks on multiplicity codes

DOI10.4086/toc.2015.v011a005zbMath1397.94127arXiv1505.07547OpenAlexW2611959999MaRDI QIDQ2941640

Swastik Kopparty

Publication date: 21 August 2015

Published in: Theory of Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.07547

zbMATH Keywords

polynomialsdifferential equationserror-correcting codesList-decoding

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Decoding (94B35)

Related Items (17)

Optimal Rate List Decoding over Bounded Alphabets Using Algebraic-geometric Codes ⋮ Derandomization from Algebraic Hardness ⋮ Explicit subspace designs ⋮ Erasures versus errors in local decoding and property testing ⋮ Improved List Decoding of Folded Reed-Solomon and Multiplicity Codes ⋮ Improved List-Decodability and List-Recoverability of Reed–Solomon Codes via Tree Packings ⋮ Generalized Singleton Bound and List-Decoding Reed–Solomon Codes Beyond the Johnson Radius ⋮ Unnamed Item ⋮ Local List Recovery of High-Rate Tensor Codes and Applications ⋮ Group homomorphisms as error correcting codes ⋮ Unnamed Item ⋮ Bounding the Number of Common Zeros of Multivariate Polynomials and Their Consecutive Derivatives ⋮ On list decoding of certain \(\mathbb{F}_q\)-linear codes ⋮ High-rate codes with sublinear-time decoding ⋮ Lifted Multiplicity Codes and the Disjoint Repair Group Property ⋮ List-Decoding with Double Samplers ⋮ Low-Density Parity-Check Codes Achieve List-Decoding Capacity

Cites Work

• List Decoding of<tex>$q$</tex>-ary Reed–Muller Codes
• Subspace evasive sets
• List decoding reed-solomon, algebraic-geometric, and gabidulin subcodes up to the singleton bound

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