7,390 research outputs found
On the Residue Codes of Extremal Type II Z4-Codes of Lengths 32 and 40
In this paper, we determine the dimensions of the residue codes of extremal
Type II Z4-codes for lengths 32 and 40. We demonstrate that every binary doubly
even self-dual code of length 32 can be realized as the residue code of some
extremal Type II Z4-code. It is also shown that there is a unique extremal Type
II Z4-code of length 32 whose residue code has the smallest dimension 6 up to
equivalence. As a consequence, many new extremal Type II Z4-codes of lengths 32
and 40 are constructed.Comment: 19 page
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
Code Design for Non-Coherent Detection of Frame Headers in Precoded Satellite Systems
In this paper we propose a simple method for generating short-length
rate-compatible codes over that are robust to non-coherent
detection for -PSK constellations. First, a greedy algorithm is used to
construct a family of rotationally invariant codes for a given constellation.
Then, by properly modifying such codes we obtain codes that are robust to
non-coherent detection. We briefly discuss the optimality of the constructed
codes for special cases of BPSK and QPSK constellations. Our method provides an
upper bound for the length of optimal codes with a given desired non-coherent
distance. We also derive a simple asymptotic upper bound on the frame error
rate (FER) of such codes and provide the simulation results for a selected set
of proposed codes. Finally, we briefly discuss the problem of designing binary
codes that are robust to non-coherent detection for QPSK constellation.Comment: 11 pages, 5 figure
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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