Maximum distance separable (MDS) matrices have applications not only in coding theory but are also of great importance in the design of block ciphers and hash functions. It is highly nontrivial to find MDS matrices which could be used in lightweight cryptography. In a SAC 2004 paper, Junod et. al. constructed a new class of efficient MDS matrices whose submatrices were circulant matrices and th...

Consider the powers of a square matrix A of order n in bottleneck algebra, where addition and multiplication are replaced by the max and min operations. The powers are periodic, starting from a certain power AK . The smallest such K is called the exponent of A and the length of the period is called the index of A. Cechlárová has characterized the matrices of index 1. Here we consider the case w...

In this paper we obtain a number of [70,35,12] singly even self-dual codes as a quasi-cyclic codes with m=2 (tailbitting convolutional codes). One of them is the first known code with parameters Beta=140 Gamma=0. All codes are not pure double circulant i.e. could not be represented in systematic form. Keywords—convolutional encoding, quasi-cyclic codes weight enumeratorg, double circulant

We consider the question of how to solve inverse problems of the form ex(0) = x(t) for an unkown matrix A, given measurements of x(t) at different time points. Problems of this form have applications in reverse engineering gene networks. In particular, we examine the cases where A is circulant and Toeplitz. We are also able to extend our findings of the circulant case to some generalizations of...

Binary embeddings provide efficient and powerful ways to perform operations on large scale data. However binary embedding typically requires long codes in order to preserve the discriminative power of the input space. Thus binary coding methods traditionally suffer from high computation and storage costs in such a scenario. To address this problem, we propose Circulant Binary Embedding (CBE) wh...

"A 4-dimensional Riemannian manifold equipped with an additional tensor structure, whose fourth power is the identity, considered. This structure has a circulant matrix respect to some basis, i.e. circulant, and it acts as isometry metric. The product associated considered studied. Conditions for metric, which imply that belongs each of basic classes Staikova-Gribachev's classi cation, are obta...