1,975 research outputs found
Residue codes of extremal Type II Z_4-codes and the moonshine vertex operator algebra
In this paper, we study the residue codes of extremal Type II Z_4-codes of
length 24 and their relations to the famous moonshine vertex operator algebra.
The main result is a complete classification of all residue codes of extremal
Type II Z_4-codes of length 24. Some corresponding results associated to the
moonshine vertex operator algebra are also discussed.Comment: 21 pages, shortened from v
Self-Dual Codes
Self-dual codes are important because many of the best codes known are of
this type and they have a rich mathematical theory. Topics covered in this
survey include codes over F_2, F_3, F_4, F_q, Z_4, Z_m, shadow codes, weight
enumerators, Gleason-Pierce theorem, invariant theory, Gleason theorems,
bounds, mass formulae, enumeration, extremal codes, open problems. There is a
comprehensive bibliography.Comment: 136 page
Conformal Designs based on Vertex Operator Algebras
We introduce the notion of a conformal design based on a vertex operator
algebra. This notation is a natural analog of the notion of block designs or
spherical designs when the elements of the design are based on self-orthogonal
binary codes or integral lattices, respectively. It is shown that the subspaces
of fixed degree of an extremal self-dual vertex operator algebra form conformal
11-, 7-, or 3-designs, generalizing similar results of Assmus-Mattson and
Venkov for extremal doubly-even codes and extremal even lattices. Other
examples are coming from group actions on vertex operator algebras, the case
studied first by Matsuo. The classification of conformal 6- and 8-designs is
investigated. Again, our results are analogous to similar results for codes and
lattices.Comment: 35 pages with 1 table, LaTe
Additive Asymmetric Quantum Codes
We present a general construction of asymmetric quantum codes based on
additive codes under the trace Hermitian inner product. Various families of
additive codes over \F_{4} are used in the construction of many asymmetric
quantum codes over \F_{4}.Comment: Accepted for publication March 2, 2011, IEEE Transactions on
Information Theory, to appea
Thermodynamic Geometry: Evolution, Correlation and Phase Transition
Under the fluctuation of the electric charge and atomic mass, this paper
considers the theory of the thin film depletion layer formation of an ensemble
of finitely excited, non-empty -orbital heavy materials, from the
thermodynamic geometric perspective. At each state of the local adiabatic
evolutions, we examine the nature of the thermodynamic parameters,
\textit{viz.}, electric charge and mass, changing at each respective
embeddings. The definition of the intrinsic Riemannian geometry and
differential topology offers the properties of (i) local heat capacities, (ii)
global stability criterion and (iv) global correlation length. Under the
Gaussian fluctuations, such an intrinsic geometric consideration is anticipated
to be useful in the statistical coating of the thin film layer of a desired
quality-fine high cost material on a low cost durable coatant. From the
perspective of the daily-life applications, the thermodynamic geometry is thus
intrinsically self-consistent with the theory of the local and global economic
optimizations. Following the above procedure, the quality of the thin layer
depletion could self-consistently be examined to produce an economic, quality
products at a desired economic value.Comment: 22 pages, 5 figures, Keywords: Thermodynamic Geometry, Metal
Depletion, Nano-science, Thin Film Technology, Quality Economic
Characterization; added 1 figure and 1 section (n.10), and edited
bibliograph
A new class of codes for Boolean masking of cryptographic computations
We introduce a new class of rate one-half binary codes: {\bf complementary
information set codes.} A binary linear code of length and dimension
is called a complementary information set code (CIS code for short) if it has
two disjoint information sets. This class of codes contains self-dual codes as
a subclass. It is connected to graph correlation immune Boolean functions of
use in the security of hardware implementations of cryptographic primitives.
Such codes permit to improve the cost of masking cryptographic algorithms
against side channel attacks. In this paper we investigate this new class of
codes: we give optimal or best known CIS codes of length We derive
general constructions based on cyclic codes and on double circulant codes. We
derive a Varshamov-Gilbert bound for long CIS codes, and show that they can all
be classified in small lengths by the building up construction. Some
nonlinear permutations are constructed by using -codes, based on the
notion of dual distance of an unrestricted code.Comment: 19 pages. IEEE Trans. on Information Theory, to appea
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