287 citations · 1.1k across the 26 of their papers we have counts for
12 papers · 1 filter
Low Rank Parity Check Codes: New Decoding Algorithms and Applications to Cryptography
Nicolas Aragon, Philippe Gaborit, Adrien Hauteville +2
We introduce a new family of rank metric codes: Low Rank Parity Check codes (LRPC), for which we propose an efficient probabilistic decoding algorithm. This family of codes can be…
LDA Lattices Without Dithering Achieve Capacity on the Gaussian Channel
Nicola di Pietro, Gilles Zémor, Joseph J. Boutros
This paper deals with Low-Density Construction-A (LDA) lattices, which are obtained via Construction A from non-binary Low-Density Parity-Check codes. More precisely, a proof is pr…
Critical pairs for the Product Singleton Bound
Diego Mirandola, Gilles Zémor
We characterize Product-MDS pairs of linear codes, i.e.\ pairs of codes whose product under coordinatewise multiplication has maximum possible minimum distance as a function…
Squares of Random Linear Codes
Ignacio Cascudo, Ronald Cramer, Diego Mirandola +1
Given a linear code , one can define the -th power of as the span of all componentwise products of elements of . A power of may quickly fill the whole space. O…
Constructions of Rank Modulation Codes
Arya Mazumdar, Alexander Barg, Gilles Zémor
Rank modulation is a way of encoding information to correct errors in flash memory devices as well as impulse noise in transmission lines. Modeling rank modulation involves constru…
Bounds for binary codes relative to pseudo-distances of k points
Christine Bachoc, Gilles Zemor
We apply Schrijver's semidefinite programming method to obtain improved upper bounds on generalized distances and list decoding radii of binary codes.
Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}
Jean-Pierre Tillich, Gilles Zemor
The current best asymptotic lower bound on the minimum distance of quantum LDPC codes with fixed non-zero rate is logarithmic in the blocklength. We propose a construction of quant…
Codes on hypergraphs
Alexander Barg, Arya Mazumdar, Gilles Zémor
Codes on hypergraphs are an extension of the well-studied family of codes on bipartite graphs. Bilu and Hoory (2004) constructed an explicit family of codes on regular t-partite hy…
Low-Density Parity-Check Codes for Nonergodic Block-Fading Channels
Joseph J. Boutros, Albert Guillen i Fabregas, Ezio Biglieri +1
We solve the problem of designing powerful low-density parity-check (LDPC) codes with iterative decoding for the block-fading channel. We first study the case of maximum-likelihood…
Asymptotic improvement of the Gilbert-Varshamov bound for linear codes
Philippe Gaborit, Gilles Zemor
The Gilbert-Varshamov bound states that the maximum size A_2(n,d) of a binary code of length n and minimum distance d satisfies A_2(n,d) >= 2^n/V(n,d-1) where V(n,d) stands for the…
On quasi-cyclic interleavers for parallel turbo codes
Joseph Boutros, Gilles Zémor
We present an interleaving scheme that yields quasi-cyclic turbo codes. We prove that randomly chosen members of this family yield with probability almost 1 turbo codes with asympt…
Distance properties of expander codes
Alexander Barg, Gilles Zemor
We study the minimum distance of codes defined on bipartite graphs. Weight spectrum and the minimum distance of a random ensemble of such codes are computed. It is shown that if th…