fully characterize the maximum-likelihood decoding (MLD) error of

an arbitrary code used over the binary erasure channel

(BEC). Based on these insights, we present a new design criterion

for a code: the

prove that, for every

codes

among all codes of equal size

Thus, it is conjectured that the fair weak flip code is

optimal in the sense of achieving the smallest MLD error over the

BEC. We confirm this conjecture for

best (in the sense of smallest MLD error)

cannot achieve the largest minimum 4-wise Hamming distance and is

thus strictly outperformed by the fair weak flip code over the

BEC.

Hamming distance, weak flip codes.

-||- _|_ _|_ / __|__ Stefan M. Moser

[-] --__|__ /__\ /__ Senior Scientist, ETH Zurich, Switzerland

_|_ -- --|- _ / / Adjunct Professor, National Yang Ming Chiao Tung University, Taiwan

/ \ [] \| |_| / \/ Web: https://moser-isi.ethz.ch/

Last modified: Tue Feb 4 13:50:42 CET 2020