منابع مشابه
Representation of Subspaces and Enumerative Encoding of the Grassmannian Space
Codes in the Grassmannian space have found recently application in network coding. Representation of kdimensional subspaces of Fq has generally an essential role in solving coding problems in the Grassmannian, and in particular in encoding subspaces of the Grassmannian. Different representations of subspaces in the Grassmannian are presented. We use two of these representations for enumerative ...
متن کاملExplicit Enumerative Geometry for the Real Grassmannian of Lines in Projective Space
For any collection of Schubert conditions on lines in projective space which generically determine a finite number of lines, we show there exist real generic conditions determining the expected number of real lines. This extends the classical Schubert calculus of enumerative geometry for the Grassmann variety of lines in projective space from the complex realm to the real. Our main tool is an e...
متن کاملEnumerative Geometry for the Real Grassmannian of Lines in Projective Space
Given Schubert conditions on lines in projective space which generically determine a nite number of lines, we show there exist general real conditions determining the expected number of real lines. This extends the classical Schubert calculus of enu-merative geometry for the Grassmann variety of lines in projec-tive space from the complex realm to the real. Our main tool is an explicit geometri...
متن کاملEnumerative Algebraic Coding for ACELP
Speech coding algorithms based on Algebraic Code Excited Linear Prediction (ACELP) quantize and code the residual signal with a fixed algebraic codebook. This paper generalizes the conventional encoding to provide optimal bit consumption for all codebook designs by enumerating all possible states. The codebook designed is aimed for constant bit-rate applications applied on mobile devices.
متن کاملEnumerative Coding for Line Polar Grassmannians
Codes arising from Grassmannians have been widely investigated, both as generalization of Reed–Muller codes and for applications to network coding. Recently we introduced some new codes, arising from Polar Grassmannians, namely the set of all subspaces of a vector space F q which are totally singular with respect to a given non-degenerate quadratic form. The aim of the present paper is to prese...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2011
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2010.2090252