Smoothing Codes and Lattices: Systematic Study and New Bounds

New upper bounds for codes correcting errors

LA Bassalygo · 1965

Earlier work this paper cites.

New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities

Robert J. McEliece, Eugene R. Rodemich, Howard Rumsey Jr., and Lloyd R. Welch · 1977

Earlier work this paper cites.

Bounds for packings on a sphere and in space

Grigory Kabatiansky and Vladimir I. Levenshtein · 1978

Earlier work this paper cites.

A Public-Key System Based on Algebraic Coding Theory

Robert J. McEliece · 1978

Earlier work this paper cites.

On bounds for packings in n n -dimensional euclidean space

Vladimir I. Levenshtein · 1979

Earlier work this paper cites.

New bounds in some transference theorems in the geometry of numbers

Wojciech Banaszczyk · 1993

Earlier work this paper cites.

Krawtchouk polynomials and universal bounds for codes and designs in hamming spaces

Vladimir I. Levenshtein · 1995

Earlier work this paper cites.

Spectral graph theory

Fan R. K. Chung · 1997

Earlier work this paper cites.

Association schemes and coding theory

Philippe Delsarte and Vladimir Iossifovitch Levenshtein · 1998

Earlier work this paper cites.

Strong asymptotics for Krawtchouk polynomials

Mourad E.H. Ismail and Plamen Simeonov · 1998

Earlier work this paper cites.

Introduction to coding theory

Jacobus Hendricus van Lint · 1999

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Estimates of the distance distribution of codes and designs

Alexei E. Ashikhmin, Alexander Barg, and Simon Litsyn · 2001

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New upper bounds on sphere packings I

Henry Cohn and Noam Elkies · 2003

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Bounds on distance distributions in codes of known size

Alexei E. Ashikhmin, Gérard D. Cohen, Michael Krivelevich, and Simon Litsyn · 2005

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Uniform bounds for bessel functions

Ilia Krasikov · 2006

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Codes for Error Detection

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Rafael Misoczki, Jean-Pierre Tillich, Nicolas Sendrier, and Paulo S. L. M. Barreto · 2013

Later among the works it cites.

Semantically secure lattice codes for the Gaussian wiretap channel

Cong Ling, Laura Luzzi, Jean-Claude Belfiore, and Damien Stehlé · 2014

Later among the works it cites.

Lattice Coding for Signals and Networks: A Structured Coding Approach to Quantization, Modulation and Multiuser Information Theory

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Later among the works it cites.

Solving the shortest vector problem in 2 n 2^{n} time using discrete Gaussian sampling

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Statistical decoding

Original

Thomas Debris-Alazard and Jean-Pierre Tillich · 2017

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