4 papers
Tensor Reed-Muller Codes: Achieving Capacity with Quasilinear Decoding Time
Emmanuel Abbe, Colin Sandon, Oscar Sprumont
Define the codewords of the Tensor Reed-Muller code to be the evaluation vectors of all multivariate polynomials in the variables $\le…
From Bit to Block: Decoding on Erasure Channels
Henry D. Pfister, Oscar Sprumont, Gilles Zémor
We provide a general framework for bounding the block error threshold of a linear code over the erasure channel in terms of its bit error threshold. Our…
A Criterion for Decoding on the BSC
Anup Rao, Oscar Sprumont
We present an approach to showing that a linear code is resilient to random errors. We use this approach to obtain decoding results for both transitive codes and Reed-Muller codes.…
List-Decoding Capacity Implies Capacity on the q-ary Symmetric Channel
Francisco Pernice, Oscar Sprumont, Mary Wootters
It is known that the Shannon capacity of the q-ary symmetric channel (qSC) is the same as the list-decoding capacity of an adversarial channel, raising the question of whether ther…