10,131 research outputs found
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
Self-Dual codes from -matrices of skew symmetric type
Previously, self-dual codes have been constructed from weighing matrices, and
in particular from conference matrices (skew and symmetric). In this paper,
codes constructed from matrices of skew symmetric type whose determinants reach
the Ehlich-Wojtas' bound are presented. A necessary and sufficient condition
for these codes to be self-dual is given, and examples are provided for lengths
up to 52
Quantum Block and Convolutional Codes from Self-orthogonal Product Codes
We present a construction of self-orthogonal codes using product codes. From
the resulting codes, one can construct both block quantum error-correcting
codes and quantum convolutional codes. We show that from the examples of
convolutional codes found, we can derive ordinary quantum error-correcting
codes using tail-biting with parameters [[42N,24N,3]]_2. While it is known that
the product construction cannot improve the rate in the classical case, we show
that this can happen for quantum codes: we show that a code [[15,7,3]]_2 is
obtained by the product of a code [[5,1,3]]_2 with a suitable code.Comment: 5 pages, paper presented at the 2005 IEEE International Symposium on
Information Theor
Self-Dual codes from (−1,1)-matrices of skew symmetric type
Previously, self-dual codes have been constructed from weighing matrices,
and in particular from conference matrices (skew and symmetric). In this paper, codes
constructed from matrices of skew symmetric type whose determinants reach the Ehlich-
Wojtas’ bound are presented. A necessary and sufficient condition for these codes to be
self-dual is given, and examples are provided for lengths up to 52.Ministerio de Ciencia e Innovación MTM2008-06578Junta de Andalucía FQM-016Junta de Andalucía P07-FQM-0298
On quadratic residue codes and hyperelliptic curves
A long standing problem has been to develop "good" binary linear codes to be
used for error-correction. This paper investigates in some detail an attack on
this problem using a connection between quadratic residue codes and
hyperelliptic curves. One question which coding theory is used to attack is:
Does there exist a c<2 such that, for all sufficiently large and all
subsets S of GF(p), we have |X_S(GF(p))| < cp?Comment: 18 pages, no figure
Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
We investigate the average bipartite entanglement, over all possible
divisions of a multipartite system, as a useful measure of multipartite
entanglement. We expose a connection between such measures and
quantum-error-correcting codes by deriving a formula relating the weight
distribution of the code to the average entanglement of encoded states.
Multipartite entangling power of quantum evolutions is also investigated.Comment: 13 pages, 1 figur
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