In this article we study the duals of Grassmann codes, certain codes coming from the Grassmannian variety. Exploiting their structure, we are able to count and classify all their minimum weight codewords. In this classification the lines lying on the Grassmannian variety play a central role. Related codes, namely the affine Grassmann codes, were introduced more recently in [1], while their dual...

A θ-local formulation of superfield Lagrangian quantization in non-Abelian hypergauges is proposed on the basis of an extension of general reducible gauge theories to special superfield models with a Grassmann parameter θ. We solve the problem of describing the quantum action and the gauge algebra of an L-stage-reducible superfield model in terms of a BRST charge for a formal dynamical system w...

Different topics on the differential geometry of the complex Grassmann manifold are surveyed in relation to the coherent states. A calculation of the tangent conjugate locus and conjugate locus in the complex Grassmann manifold is presented. The proofs use the Jordan’s stationary angles. Also various formulas for the distance on the complex Grassmann manifold are furnished.

How can video clips be analyzed to describe organic human actions automatically? How can the long-wave infrared spectrum of an underwater object be identified when the water is distorting the signature of the target? If you had the reflection of an image from a fun-house mirror, could you recognize the original image? My research focuses on geometric analysis of high dimensional data, and inclu...

This paper characterizes the effect of finite rate channel state feedback on the sum rate of a multi-access multiple-input multiple-output (MIMO) system. We propose to control the users jointly, specifically, we first choose the users jointly and then select the corresponding beamforming vectors jointly. To quantify the sum rate, this paper introduces the composite Grassmann manifold and the co...

Generalized Zk-graded Grassmann variables are used to label coherent states related to the nilpotent representation of the q-oscillator of Biedenharn and Macfarlane when the deformation parameter is a root of unity. These states are then used to construct generalized Grassmann representatives of state vectors. Recently in [1] we have constructed coherent states for k-fermions using Kerner’s [2]...

This paper shows that the Grassmann Manifolds GF(n,N) can all be imbedded in an Euclidean space MF(N) naturally and the imbedding can be realized by the eigenfunctions of Laplacian △ on GF(n,N). They are all minimal submanifolds in some spheres of MF(N) respectively. Using these imbeddings, we construct some degenerate Morse functions on Grassmann Manifolds, show that the homology of the comple...

A bstract Celestial amplitude is a new reformulation of momentum space scattering amplitudes and offers promising way for flat holography. In this paper, we study the celestial in $$ \mathcal{N} N = 4 Super-Yang-Mills (SYM) theory aiming at understanding role superconformal symmetry We first construct generat...