Further improvements on the Feng-Rao bound for dual codes

Published 6 May 2013 in cs.IT, math.AC, math.AG, and math.IT | (1305.1091v1)

Abstract: Salazar, Dunn and Graham in [Salazar et. al., 2006] presented an improved Feng-Rao bound for the minimum distance of dual codes. In this work we take the improvement a step further. Both the original bound by Salazar et. al., as well as our improvement are lifted so that they deal with generalized Hamming weights. We also demonstrate the advantage of working with one-way well-behaving pairs rather than weakly well-behaving or well-behaving pairs.