7 research outputs found
Primal-dual distance bounds of linear codes with application to cryptography
Let denote the minimum length of a linear code with
and , where is the minimum Hamming distance of and
is the minimum Hamming distance of . In this paper, we
show a lower bound and an upper bound on . Further, for small
values of and , we determine and give a generator
matrix of the optimum linear code. This problem is directly related to the
design method of cryptographic Boolean functions suggested by Kurosawa et al.Comment: 6 pages, using IEEEtran.cls. To appear in IEEE Trans. Inform. Theory,
Sept. 2006. Two authors were added in the revised versio
Results on Binary Linear Codes With Minimum Distance 8 and 10
All codes with minimum distance 8 and codimension up to 14 and all codes with
minimum distance 10 and codimension up to 18 are classified. Nonexistence of
codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new
exact bounds for binary linear codes. Primarily two algorithms considering the
dual codes are used, namely extension of dual codes with a proper coordinate,
and a fast algorithm for finding a maximum clique in a graph, which is modified
to find a maximum set of vectors with the right dependency structure.Comment: Submitted to the IEEE Transactions on Information Theory, May 2010 To
be presented at the ACCT 201
A simple combinatorial treatment of constructions and threshold gaps of ramp schemes
We give easy proofs of some recent results concerning threshold gaps in ramp schemes. We then generalise a construction method for ramp schemes employing error-correcting codes so that it can be applied using nonlinear (as well as linear) codes. Finally, as an immediate consequence of these results, we provide a new explicit bound on the minimum length of a code having a specified distance and dual distance
The degree of a Boolean function and some algebraic properties of its support
In this paper, the support of a Boolean function is used to establish some algebraic properties. These properties allow the degree of a Boolean function to be obtained without having to calculate its algebraic normal form. Furthermore, some algorithms are derived and the average time computed to obtain the degree of some Boolean functions from its support.Partially supported by Spanish grant MTM2011-24858 of the Ministerio de Economía y Competitividad of the Gobierno de España and by the research project UMH-Bancaja with reference IPZS01
Primal-Dual Distance Bounds of Linear Codes With Application To Cryptography
We propose upper and lower bounds on the minimum code length of linear codes with specified minimum Hamming distance and dual distance. From thes