Involutions on the the Barnes-Wall lattices and their fixed point sublattices, I

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dc.creatorGriess Jr, Robert L.
dc.date2005-11-03
dc.date.accessioned2026-07-07T06:50:44Z
dc.date.available2026-07-07T06:50:44Z
dc.descriptionWe study the sublattices of the rank $2^d$ Barnes-Wall lattices $\bw d$ which occur as fixed points of involutions. They have ranks $2^{d-1}$ (for dirty involutions) or $2^{d-1}\pm 2^{k-1}$ (for clean involutions), where $k$, the defect, is an integer at most $\frac d 2$. We discuss the involutions on $\bw d$ and determine the isometry groups of the fixed point sublattices for all involutions of defect 1. Transitivity results for the Bolt-Room-Wall group on isometry types of sublattices extend those in \cite{bwy}. Along the way, we classify the orbits of $AGL(d,2)$ on the Reed-Muller codes $RM(2,d)$ and describe {\it cubi sequences} for short codewords, which give them as Boolean sums of codimension 2 affine subspaces.
dc.description39 pages
dc.identifierhttps://arxiv.org/abs/math/0511084
dc.identifierhttp://arxiv.org/abs/math/0511084
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/104757
dc.subjectGroup Theory
dc.subjectNumber Theory
dc.subject11H56
dc.titleInvolutions on the the Barnes-Wall lattices and their fixed point sublattices, I
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