New parameters of subsets in polynomial schemes
Abstract
We define new parameters, a zero interval and a dual zero interval, of subsets in - or -polynomial schemes. A zero interval of a subset in a -polynomial scheme is a successive interval index for which the inner distribution vanishes, and a dual zero interval of a subset in a -polynomial scheme is a successive interval index for which the dual inner distribution vanishes. We derive the bounds of the lengths of a zero interval and a dual zero interval using the degree and dual degree respectively, and show that a subset in a -polynomial scheme (resp. a -polynomial scheme) having a large length of a zero interval (resp. a dual zero interval) induces a completely regular code (resp. a -polynomial scheme). Moreover, we consider the spherical analogue of a dual zero interval.
Cite
@article{arxiv.1008.0189,
title = {New parameters of subsets in polynomial schemes},
author = {Sho Suda},
journal= {arXiv preprint arXiv:1008.0189},
year = {2010}
}