Counting Functions and Expected Values for the k-Error Linear Complexity

Counting Functions for the k-Error Linear Complexity of 2-Periodic Binary Sequences

Linear complexity is an important measure of the cryptographic strength of key streams used in stream ciphers. The linear complexity of a sequence can decrease drastically when a few symbols are changed. Hence there has been considerable interest in the k-error linear complexity of sequences which measures this instability in linear complexity. For 2-periodic sequences it is known that minimum ...

Counting Functions for the k-Error Linear Complexity of 2n-Periodic Binary Sequences

$k$-Error linear complexity for multidimensional arrays

In this paper, we focus on linear complexity measures of multidimensional sequences over finite fields, generalizing the one-dimensional case and including that of multidimensional arrays (identified with multidimensional periodic sequence) as a particular instance. A cryptographically strong sequence or array should not only have a high linear complexity, it should also not be possible to decr...

Generalization Error and the Expected Network Complexity

For two layer networks with n sigmoidal hidden units, the generalization error is shown to be bounded by O(E~) O( (EK)d l N) K + N og , where d and N are the input dimension and the number of training samples, respectively. E represents the expectation on random number K of hidden units (1 :::; I\ :::; n). The probability Pr(I{ = k) (1 :::; k :::; n) is (kt.erl11ined by a prior distribution of ...

On the k-error linear complexity of cyclotomic sequences

Exact values and bounds on the k-error linear complexity of p-periodic sequences which are constant on the cyclotomic classes are determined. This family of sequences includes sequences of discrete logarithms, Legendre sequences and Hall’s sextic residue sequence.