Related papers: The construction and weight distributions of all p…
A random construction of bipolar sensing matrices based on binary linear codes is introduced and its RIP (Restricted Isometry Property) is analyzed based on an argument on the ensemble average of the weight distribution of binary linear…
In this paper some cryptographic properties of Boolean functions, including weight, balancedness and nonlinearity, are studied, particularly focusing on splitting functions and cubic Boolean functions. Moreover, we present some quantities…
The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences…
Boolean functions are mathematical objects used in diverse domains and have been actively researched for several decades already. One domain where Boolean functions play an important role is cryptography. There, the plethora of settings one…
A pairing function for the non-negative integers is said to be binary perfect if the binary representation of the output is of length 2k or less whenever each input has length k or less. Pairing functions with square shells, such as the…
We study the use of binary activated neural networks as interpretable and explainable predictors in the context of regression tasks on tabular data; more specifically, we provide guarantees on their expressiveness, present an approach based…
Few-weight codes have been constructed and studied for many years, since their fascinating relations to finite geometries, strongly regular graphs and Boolean functions. Simplex codes are one-weight Griesmer $[\frac{q^k-1}{q-1},k…
The duals of cyclic codes with two zeros have been extensively studied, and their weight distributions have recently been evaluated in some cases. In this note, we determine the weight distribution of a certain new class of such codes by…
The beta distribution is a basic distribution serving several purposes. It is used to model data, and also, as a more flexible version of the uniform distribution, it serves as a prior distribution for a binomial probability. The bivariate…
In decoding linear block codes, it was shown that noticeable reliability gains can be achieved by introducing learnable parameters to the Belief Propagation (BP) decoder. Despite the success of these methods, there are two key open…
For every linear binary code $C$, we construct a geometric triangular configuration $\Delta$ so that the weight enumerator of $C$ is obtained by a simple formula from the weight enumerator of the cycle space of $\Delta$. The triangular…
In this paper we compute the Fourier spectra of some recently discovered binomial APN functions. One consequence of this is the determination of the nonlinearity of the functions, which measures their resistance to linear cryptanalysis.…
Due to their important applications to coding theory, cryptography, communications and statistics, combinatorial $t$-designs have been attracted lots of research interest for decades. The interplay between coding theory and $t$-designs has…
Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive…
Since the 90's, several authors have studied a probability distribution on the set of Boolean functions on $n$ variables induced by some probability distributions on formulas built upon the connectors $And$ and $Or$ and the literals…
We study the inverse spectral problem for weighted projective spaces using wave-trace methods. We show that in many cases one can "hear" the weights of a weighted projective space.
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
There are several methods for constructing secret sharing schemes, one of which is based on coding theory. Theoretically, every linear code can be used to construct secret sharing schemes. However, in general, determining the access…
We construct a class of three-Lee-weight and two infinite families of five-Lee-weight codes over the ring $R=\mathbb{F}_2 +v\mathbb{F}_2 +v^2\mathbb{F}_2 +v^3\mathbb{F}_2 +v^4\mathbb{F}_2,$ where $v^5=1.$ The same ring occurs in the quintic…
We present a novel technique for encoding and decoding constant weight binary codes that uses a geometric interpretation of the codebook. Our technique is based on embedding the codebook in a Euclidean space of dimension equal to the weight…