scholarly journals Properties of codes with two homogeneous weights

2012 ◽  
Vol 18 (4) ◽  
pp. 711-727 ◽  
Author(s):  
Eimear Byrne ◽  
Michael Kiermaier ◽  
Alison Sneyd
Keyword(s):  
Homogeneous Weights

scholarly journals Sharp Multidimensional Multiplicative Inequalities for Weighted L_p Spaces with Homogeneous Weights

1998 ◽  
pp. 53-67 ◽  
Author(s):  
Sorina Barza ◽  
Victor Burenkov ◽  
Josip Pečarić ◽  
Lars-Erik Persson
Keyword(s):  
Homogeneous Weights

scholarly journals The homogeneous weight for Rk, related gray map and new binary quasi-cyclic codes

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 885-897 ◽  
Author(s):  
Bahattin Yildiz ◽  
Ismail Kelebek
Keyword(s):  
Coding Theory ◽  
Cyclic Codes ◽  
Gray Map ◽  
Binary Codes ◽  
Binary Images ◽  
Frobenius Rings ◽  
Homogeneous Weights ◽  
Homogeneous Weight ◽  
Theoretical Results ◽  
Quasi Cyclic Codes

Using theoretical results about the homogeneous weights for Frobenius rings, we describe the homogeneous weight for the ring family Rk, a recently introduced family of Frobenius rings which have been used extensively in coding theory. We find an associated Gray map for the homogeneous weight using first order Reed-Muller codes and we describe some of the general properties of the images of codes over Rk under this Gray map. We then discuss quasi-twisted codes over Rk and their binary images under the homogeneous Gray map. In this way, we find many optimal binary codes which are self-orthogonal and quasi-cyclic. In particular, we find a substantial number of optimal binary codes that are quasi-cyclic of index 8, 16 and 24, nearly all of which are new additions to the database of quasi-cyclic codes kept by Chen.

scholarly journals Sharp quantitative stability for isoperimetric inequalities with homogeneous weights

2022 ◽  
Author(s):  
E. Cinti ◽  
F. Glaudo ◽  
A. Pratelli ◽  
X. Ros-Oton ◽  
J. Serra
Keyword(s):  
Isoperimetric Inequalities ◽  
Quantitative Stability ◽  
Homogeneous Weights

scholarly journals Homogeneous weights and exponential sums

2003 ◽  
Vol 9 (3) ◽  
pp. 310-321 ◽  
Author(s):  
José Felipe Voloch ◽  
Judy L. Walker
Keyword(s):  
Exponential Sums ◽  
Homogeneous Weights

scholarly journals Hardy inequalities with homogeneous weights

2015 ◽  
Vol 268 (11) ◽  
pp. 3278-3289 ◽  
Author(s):  
Thomas Hoffmann-Ostenhof ◽  
Ari Laptev
Keyword(s):  
Hardy Inequalities ◽  
Homogeneous Weights

Sharp weighted isoperimetric and Caffarelli–Kohn–Nirenberg inequalities

2017 ◽  
Vol 0 (0) ◽  
Author(s):  
Nguyen Lam
Keyword(s):  
Conformal Mapping ◽  
Mass Transport ◽  
Ricci Tensor ◽  
Weight Functions ◽  
Optimal Mass Transport ◽  
Homogeneous Weights ◽  
Transport Method

AbstractUsing the optimal mass transport method and a suitable quasi-conformal mapping, we study the sharp weighted isoperimetric, Sobolev, Gagliardo–Nirenberg and Caffarelli–Kohn–Nirenberg inequalities. The class of weight functions under consideration includes all nonnegative homogeneous weights satisfying a concavity condition that is equivalent to a usual curvature-dimension bound and the nonnegativity of a Bakry–Émery Ricci tensor. Though our densities are not radial in general, the optimizers are radially symmetric.

On p-Ary Local Frobenius Rings and their Homogeneous Weights

2016 ◽  
Vol 10 (6) ◽  
pp. 2109-2116
Author(s):  
Bahattin Yildiz ◽  
Makarim Abdlwahed Abdljabbar
Keyword(s):  
Frobenius Rings ◽  
Homogeneous Weights

scholarly journals PHASE TRANSITIONS IN ISING MODEL INDUCED BY WEIGHT REDISTRIBUTION ON WEIGHTED REGULAR NETWORKS

2013 ◽  
Vol 27 (26) ◽  
pp. 1350146 ◽  
Author(s):  
MENGHUI LI ◽  
YING FAN ◽  
JINSHAN WU ◽  
ZENGRU DI
Keyword(s):  
Phase Transition ◽  
Collective Behavior ◽  
Topological Structure ◽  
Dynamical Behaviors ◽  
Link Weight ◽  
Shortest Distance ◽  
Homogeneous Weights ◽  
Additional Approach ◽  
Regular Networks

In order to investigate the role of link weight in weighted networks, the collective behavior of an Ising system on weighted regular networks is studied by numerical simulation. In our model, the coupling strength between spins is inversely proportional to the corresponding weighted shortest distance. Disordering link weights can effectively affect the process of phase transition even though the underlying binary topological structure remains unchanged. Specifically, based on regular networks with homogeneous weights initially, randomly disordering link weights will change the critical temperature of phase transition. The results suggest that the redistribution of link weights may provide an additional approach to optimize the dynamical behaviors of the system.

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