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Subspace codes in PG(2n-1,q) [article]

Antonio Cossidente, Francesco Pavese
2014 arXiv   pre-print
Constant--dimension subspace codes gained recently lot of interest due to the work by Koetter and Kschischang, where they presented an application of such codes for error-correction in random network coding  ...  Here a (2n,M,4;n)_q constant--dimension subspace code is constructed, for every n > 4. The size of our codes is considerably larger than all known constructions so far, whenever n > 4.  ...  Let A be a n × n matrix over GF(q), and let I n be the n × n identity matrix.  ... 
arXiv:1411.3601v1 fatcat:z43stevrmfbprntytd3xbygxsi

Subspace Codes in PG(2N − 1, Q)

Antonio Cossidente, Francesco Pavese
2016 Combinatorica  
Constant-dimension subspace codes gained recently lot of interest due to the work by Koetter and Kschischang [18], where they presented an application of such codes for error-correction in random network  ...  Here a (2n, M, 4; n) q constant-dimension subspace code is constructed, for every n ≥ 4. The size of our codes is considerably larger than all known constructions so far, whenever n > 4.  ...  Let A be a n × n matrix over GF(q), and let I n be the n × n identity matrix.  ... 
doi:10.1007/s00493-016-3354-5 fatcat:g63lsx55mfex3nts6df4euu5za

Non-local charges and quantum integrability of sigma models on the symmetric spaces SO(2n)/SO(n)×SO(n) and Sp(2n)/Sp(n)×Sp(n)

J.M Evans, D Kagan, C.A.S Young
2004 Physics Letters B  
Non-local conserved charges in two-dimensional sigma models with target spaces SO(2n)/SO(n)×SO(n) and Sp(2n)/Sp(n)×Sp(n) are shown to survive quantization, unspoiled by anomalies; these theories are therefore  ...  Local, higher-spin, conserved charges are also shown to survive quantization in the SO(2n)/SO(n)×SO(n) models.  ...  Acknowledgements The research of J.M.E. is supported in part by Gonville and Caius College, Cambridge. C.A.S.Y. is supported by a PPARC studentship.  ... 
doi:10.1016/j.physletb.2004.04.042 fatcat:cn4qnlepknbmvjeuouxsnnle3y

Quadratic Cycles on GL(2n) Cusp Forms

Y.Z. Flicker
1995 Journal of Algebra  
It is based on integrating the kernel of the convolution operator K f x; y o v er x and y in two cycles ZC 1 nC 1 and ZC 2 nC 2 .  ...  The case of the group C C and the subgroups C 1 = C 2 = C embedded diagonally, coincides with the standard trace formula.  ...  The proofs of BDKV , F2 , F1; III and FK1 are based on the Deligne-Kazhdan" simple trace formula, and that of FK2 on a sharper form of the simple trace formula, where regular, Iwahori-invariant functions  ... 
doi:10.1006/jabr.1995.1146 fatcat:lv6duvgedvafxfht4h7d2i6eme

Automorphisms and Equivalence of Bent Functions and of Difference Sets in Elementary Abelian 2-Groups

U. Dempwolff
2006 Communications in Algebra  
We describe some series of such sets and compute their automorphism group.  ...  For some of these sets the construction is based on the nonvanishing of the degree 1-chohomology of certain Chevalley groups in characteristic two.  ...  This package was essential for the computations of the previous section. It was also very useful for the theoretical results as computations in small cases often indicated a general statement.  ... 
doi:10.1080/00927870500442062 fatcat:p7fe534pwjgn5gpf6c5genmjfq

Error resilient MPEG-2 video coding schemes based on three layer error control coding

Changseok Bae, Jeunwoo Lee, Vera Chung
2006 2006 8th International Conference Advanced Communication Technology  
Design of error-control coding schemes for three problems of noisy information transmission, storage and processing. Eindhoven: Technische Universiteit Eindhoven. https://doi.org/10.6100/IR274904  ...  Acknowledgment This paper is based on the author's Master's Thesis [4] Acknowledgment The author wishes to thank one of the anonymous referees for pointing out to him Vasil'ev's construction [12] which  ...  leads to Construction 3B and Example 3.  ... 
doi:10.1109/icact.2006.206270 fatcat:bqbplmz4nfe73evaekbv776kni

Legendrian Submanifolds in R^2n+1 and Contact Homology [article]

Tobias Ekholm, John Etnyre, Michael G. Sullivan
2002 arXiv   pre-print
In a sense, the definition of contact homology presented in this paper is a high dimensional analog of the work of Chekanov and others on Legendrian 1-knots in 3-space.  ...  For example, infinite families of pairwise non-isotopic Legendrian n-spheres and n-tori, which are indistinguishable by means of previously known invariants, are constructed.  ...  ) and its trace∂u|∂D m lies in H 1 2 (D m , T * 0,1 D m ⊗ C n )).  ... 
arXiv:math/0210124v3 fatcat:x5jmeedjpvdbdnitxeak6d3wlu

Approximate Randomization of Quantum States With Fewer Bits of Key

Paul A. Dickinson, Ashwin Nayak
2006 AIP Conference Proceedings  
Our bound is a log d factor smaller than that of Hayden, Leung, Shor, and Winter (2004), and Ambainis and Smith (2004).  ...  We present an improved, efficient construction of an approximately randomizing map that uses O(d/epsilon^2) Pauli operators to map any d-dimensional state to a state that is within trace distance epsilon  ...  Acknowledgements We thank Debbie Leung, Harold Ollivier, and David Woodruff for helpful discussions, Noga Alon for providing a copy of [2] , and Alfred Menezes and Jeff Shallit for pointers to the literature  ... 
doi:10.1063/1.2400876 fatcat:pyejgozcl5c5bgbxohgxsjggrq

Mutually unbiased bases, generalized spin matrices and separability

Arthur O. Pittenger, Morton H. Rubin
2004 Linear Algebra and its Applications  
1/d : | v, w | 2 = 1 d .  ...  Additionally we give formulas from which the orthogonal bases can be readily computed. We show how the techniques developed here provide a natural way to analyze the separability of the bases.  ...  Then V 2 (GF(p n )) can be written as a 2n-dimensional space over Z p .  ... 
doi:10.1016/j.laa.2004.04.025 fatcat:xzp5ehmrtndlfi7fvbdn2lud24

The LU-LC conjecture, diagonal local operations and quadratic forms over GF(2) [article]

D. Gross, M. Van den Nest
2007 arXiv   pre-print
Furthermore, the reduced version of the problem, involving such diagonal local operations, is mapped to questions regarding quadratic forms over the finite field GF(2).  ...  The contribution of this paper is a reduction of the LU-LC conjecture to a simpler problem - which, however, remains to date unsolved.  ...  This work has been supported by the European Union (QICS, OLAQUI, SCALA, QAP, EURYI grant of J. Eisert), the FWF, and the EPSRC (IRC QIC).  ... 
arXiv:0707.4000v2 fatcat:7rkm7wxz4rcxtkovgwcnps2sgy

Wigner functions and separability for finite systems

Arthur O Pittenger, Morton H Rubin
2005 Journal of Physics A: Mathematical and General  
A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented.  ...  This is in contrast to the more usual choice of a two-dimensional phase space containing p^(2n) points.  ...  In addition, there is a trace operation defined on GF (p n ) that is linear over GF (p) and that maps GF (p n ) to GF (p).  ... 
doi:10.1088/0305-4470/38/26/012 fatcat:m6z7anyszzdvrj3cvvbdmm2sgy

Mutually Unbiased Bases, Generalized Spin Matrices and Separability [article]

Arthur O. Pittenger, Morton H. Rubin
2004 arXiv   pre-print
A collection of orthonormal bases for a complex dXd Hilbert space is called mutually unbiased (MUB) if for any two vectors v and w from different bases the square of the inner product equals 1/d: || ^2  ...  Additionally we give formulas from which the orthogonal bases can be readily computed. We show how the techniques developed here provide a natural way to analyze the separability of the bases.  ...  trace operation and dual bases.  ... 
arXiv:quant-ph/0308142v2 fatcat:qpc5cchtafbbxhfj3sfigbzoa4

Constructive recognition of classical groups in odd characteristic

C.R. Leedham-Green, E.A. O'Brien
2009 Journal of Algebra  
Let G = X GL(d, F ) be a classical group in its natural representation defined over a finite field F of odd characteristic.  ...  The algorithms run in polynomial-time, subject to the existence of a discrete logarithm oracle for F .  ...  We can write G over GF(q) by conjugating G by a diagonal matrix diag(α, 1) where α is an element of trace 0 in GF(q 2 ); alternatively we could use the algorithm of [22] ; either requires O (log q) field  ... 
doi:10.1016/j.jalgebra.2009.04.028 fatcat:2sbas3gmufbbldoyiwhqn6ygpe

Multi-letter Youden rectangles from quadratic forms

Peter J. Cameron
2003 Discrete Mathematics  
Some infinite families of systems of linked symmetric designs (or SLSDs, for short) were constructed by Cameron and Seidel [3] using quadratic and bilinear forms over GF(2).  ...  These rectangles are k × v, with v = 2 2n and k = 2 2n−1 ± 2 n−1 .  ...  Bailey and D. A. Preece for explanations, comments, and access to their reprint collections.  ... 
doi:10.1016/s0012-365x(02)00804-x fatcat:bkgjptjur5gofj6pfjljpeio74

Low complexity normal bases

David W. Ash, Ian F. Blake, Scott A. Vanstone
1989 Discrete Applied Mathematics  
In GF(2'") squaring with respect to a normal basis representation becomes simply a cyclic shift of the vector. For hardware design this is one of the very attractive features of these bases.  ...  In this paper we investigate low complexity normal bases, give a construction for such bases and apply it to a number of cases of interest.  ...  , California Institute of Technology, with regard to Algorithm 2.7 and Theorem 2.2 respectively.  ... 
doi:10.1016/0166-218x(89)90001-2 fatcat:i44sqckagbdgtays6mnjiz2t24
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