Small weight bases for Hamming codes

AbstractWe present constructions of bases for a Hamming code having small width and height, i.e. number of 1s in each row and column in the corresponding matrix. Apart from being combinatorially interesting in their own right, these bases also lead to improved embeddings of a hypercube of cliques into a same-sized hypercube

Inferring a DNA sequence from erroneous copies

AbstractWe suggest a novel approach for efficiently reconstructing an original DNA sequence from erroneous copies