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Almost all self-dual codes are rigid

Haluk Oral, Kevin T Phelps
1992 Journal of combinatorial theory. Series A  
We prove that almost every binary self-dual code has trivial automorphism group. We also construct a self-dual code with trivial automorphism group. :G  ...  We will prove that almost all self-dual (binary) codes are rigid. We are only considering binary linear codes of even length and log always is log,.  ...  EXAMPLE OF RIGID SELF-DUAL CODE We have a seeming anomaly in that almost all self-dual codes are rigid, but (until very recently [6] ) there were no known (published) examples.  ... 
doi:10.1016/0097-3165(92)90007-h fatcat:lcdsmjbcifh7deqakykihbu6ya

Page 1184 of Mathematical Reviews Vol. , Issue 93b [page]

1993 Mathematical Reviews  
that is, which are orphans.” 93b:94022 94B05 11T71 Oral, Haluk (1-ABRN-AL); Phelps, Kevin T. (1-ABRN-AL) Almost all self-dual codes are rigid.  ...  We only consider binary linear codes of even length. We prove that almost all self-dual (binary) codes are rigid.” 93b:94023 94B15 Barg, Alexander M.; Dumer, Ilya I. [Dumer, I. I.]  ... 

Page 2407 of Mathematical Reviews Vol. , Issue 94d [page]

1994 Mathematical Reviews  
2407 not rigid is at least 3 —e. On the other hand, if 2+elogn<d< n—(2+e), then almost all d-dimensional codes are rigid. The paper consists of three parts.  ...  Here we are able to construct similar self-dual codes in arbitrary characteristic.” 94d:94019 94B27 11T71 14H55 Garcia, Arnaldo (BR-IMPA; Rio de Janeiro); Kim, Seon Jeong (KR-GYSG; Chinju); Lax, Robert  ... 

On the automorphism groups of binary linear codes [article]

Martino Borello
2013 arXiv   pre-print
Finally we give a short survey on the problem of determining the automorphism group of a putative self-dual [72,36,16] code, in order to show where these methods can be applied.  ...  In this paper we collect some answers to this question in the cases G=C_p, G=C_2p and G=D_2p (p an odd prime), with a particular regard to the case in which C is self-dual.  ...  Then the following are equivalent: a) C is self-dual. b) π σ (C(σ)) is self-dual and ϕ p (E(σ) * ) is Hermitian self-dual. Remark 2.3.  ... 
arXiv:1311.3868v1 fatcat:wgnl6z6q3bblxnbqharynhqez4

Modeling Mixtures of Different Mass Ultracold Atoms in Optical Lattices: An Illustration of High Efficiency and Linear Scaling on the Cray XT4 via a Capability Applications Project at ERDC

J.K. Freericks
2008 2008 DoD HPCMP Users Group Conference  
The theoretical maximum speed up (linear curve) is compared to the dual core (black line with circles) and quad core (red line with squares) One can immediately see that the code is giving almost perfect  ...  to the master; 4) once all Matsubara frequency calculations are complete, the master sends each slave node the local Green's function and the self-energy for a fixed lattice site and all Matsubara frequencies  ... 
doi:10.1109/dod.hpcmp.ugc.2008.38 fatcat:kix4air5wrhrlipsbilroepjde

Page 1698 of Psychological Abstracts Vol. 76, Issue 6 [page]

1989 Psychological Abstracts  
Resulis support bilingual dual coding theory as proposed by Paivio and A. Desrochers (see PA, Vol 67:2758). (French abstract) 17878. Auday, Bryan C.; Sullivan, Christopher & Cross, Henry A.  ...  —Since the literature regarding memory indicates that short-term, short- term with rehearsal, and long-term memories are all distinct, listening tasks were devised to utilize these 3 different kinds of  ... 

Dual Geometric Graph Network (DG2N) – Iterative network for deformable shape alignment [article]

Dvir Ginzburg, Dan Raviv
2021 arXiv   pre-print
We provide a novel new approach for aligning geometric models using a dual graph structure where local features are mapping probabilities.  ...  Here we propose to rethink this task and use unrolling concepts on a dual graph structure - one for a forward map and one for a backward map, where the features are pulled back matching probabilities from  ...  to the fact we are self-supervised and shape-pair specific, thus are almost invariant to noise No post processing filters are used for any of the methods except the specified refinement procedures.  ... 
arXiv:2011.14723v2 fatcat:b7mamrybkjbzviihmik2gcbcdm

Self Duality and Codings for Expansive Group Automorphisms [article]

Alex Clark, Robbert Fokkink
2005 arXiv   pre-print
The constructions naturally lead to an almost 1-1-coding of certain Pisot automorphisms by their associated β-shift, generalizing similar results for Pisot automorphisms of the torus.  ...  Lind and Schmidt have shown that the homoclinic group of a cyclic ^k algebraic dynamical system is isomorphic to the dual of the phase group.  ...  By Corollary 5 the homoclinic group Ω is isomorphic to the dual of Γ. So to establish self duality of the sequence, we need to show that Ω + and Ω − are self-dual.  ... 
arXiv:math/0501469v1 fatcat:mqbembgyb5dqvexjlcptgeuwmm

Page 6 of Eclectic Magazine of Foreign Literature Vol. 45, Issue 1 [page]

1858 Eclectic Magazine of Foreign Literature  
Hegel has acutely remarked, that history and a State almost imply each other, and are the reciprocal conditions of each other’s existence.  ...  Such a beauty we find also in its loveliest form in the Indian world; a beauty of enervation, in which all that is rough, rigid, and contradictory is dis¬ solved, and we have only the soul in a stite of  ... 

A primer on substitution tilings of the Euclidean plane [article]

Natalie Priebe Frank
2007 arXiv   pre-print
For our purposes, tiling substitution rules are divided into two broad classes: geometric and combinatorial.  ...  Combinatorial substitutions are just beginning to be examined, and some of what we present here is new.  ...  This is a relatively strong property, and one that is almost always assumed in the literature. All of the substitutions in the paper are primitive except Examples 3 and 34.  ... 
arXiv:0705.1142v1 fatcat:wcwenhi5crhtxc2gmrc5yqttbm

Maximum Variance Hashing via Column Generation

Lei Luo, Chao Zhang, Yongrui Qin, Chunyuan Zhang
2013 Mathematical Problems in Engineering  
The idea is to maximize the total variance of the hash codes while preserving the local structure of the training data.  ...  It works on the basis that the sequence of restrict primal problems all have the same dual in which the most violated constraint indicates the steepest ascent direction of the dual.  ...  in the dual are satisfied, which means that no new hash function can be generated.  ... 
doi:10.1155/2013/379718 fatcat:ztdc6jjmfnbtjpy2ftrw3cprky

Hadamard Matrices and Their Designs: A Coding-Theoretic Approach

E. F. Assmus, J. D. Key
1992 Transactions of the American Mathematical Society  
We study these, and other classes of designs associated with Hadamard matrices, using the tools of algebraic coding theory and the customary association of linear codes with designs.  ...  are self-dual. 3.6 General constructions.  ...  Clearly, both these Hadamard designs are self dual, B being symmetric.  ... 
doi:10.2307/2154164 fatcat:ddpjtkhtkndmlm5xt6pxu3kbli

The moment map of a Lie group representation

N. J. Wildberger
1992 Transactions of the American Mathematical Society  
We study these, and other classes of designs associated with Hadamard matrices, using the tools of algebraic coding theory and the customary association of linear codes with designs.  ...  are self-dual. 3.6 General constructions.  ...  Clearly, both these Hadamard designs are self dual, B being symmetric.  ... 
doi:10.1090/s0002-9947-1992-1040046-6 fatcat:f5xlybg4rfba3be7tyvl6xcz2e

A primer of substitution tilings of the Euclidean plane

Natalie Priebe Frank
2008 Expositiones mathematicae  
For our purposes, tiling substitution rules are divided into two broad classes: geometric and combinatorial.  ...  Combinatorial substitutions are just beginning to be examined, and some of what we present here is new.  ...  This is a relatively strong property, and one that is almost always assumed in the literature. All of the substitutions in the paper are primitive except Examples 3 and 19.  ... 
doi:10.1016/j.exmath.2008.02.001 fatcat:a2mwek5iizd7vfg7hb72xy5vw4

Elasticity-inspired deformers for character articulation

Ladislav Kavan, Olga Sorkine
2012 ACM Transactions on Graphics  
a) (b) (c) (d) (e) BBW Our method Our method LBS DQS Figure 1 : Previous automatic weighting schemes, such as bounded biharmonic weights (BBW) are deformation-agnostic, whereas our method optimizes weights  ...  Combined with our joint-based deformers, we achieve higher-quality results than both linear blend (LBS) and dual quaternion skinning (DQS).  ...  Acknowledgements We are grateful to Chris Evans and John Howe for art and rigging feedback.  ... 
doi:10.1145/2366145.2366215 fatcat:zw3gbib5fzdinheon767zm2f7y
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