Related papers: A Construction of Binary Linear Codes from Boolean…
We consider the problem of linearizing a pseudo-Boolean function $f : \{0,1\}^n \to \mathbb{R}$ by means of $k$ Boolean functions. Such a linearization yields an integer linear programming formulation with only $k$ auxiliary variables. This…
A new construction of codes from old ones is considered, it is an extension of the matrix-product construction. Several linear codes that improve the parameters of the known ones are presented.
This survey provides a comprehensive overview of the study of the binary and Boolean rank from both a mathematical and a computational perspective, with particular emphasis on their relationship to the real rank. We review the basic…
Binary matrix codes with restricted row and column weights are a desirable method of coded modulation for power line communication. In this work, we construct such matrix codes that are obtained as products of affine codes - cosets of…
For three decades binary decision diagrams, a data structure efficiently representing Boolean functions, have been widely used in many distinct contexts like model verification, machine learning, cryptography and also resolution of…
Rotation symmetric Boolean functions represent an interesting class of Boolean functions as they are relatively rare compared to general Boolean functions. At the same time, the functions in this class can have excellent properties, making…
In [4] we describe a variation of the classical permutation decoding algorithm that can be applied to any binary affine-invariant code; in particular, it can be applied to first-order Reed-Muller codes successfully. In this paper we study…
We define tests of boolean functions which distinguish between linear (or quadratic) polynomials, and functions which are very far, in an appropriate sense, from these polynomials. The tests have optimal or nearly optimal trade-offs between…
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…
The objective of this paper is to construct a class of linear codes with two nonzero weights and three nonzero weights by using the general trace functions, which weight distributions has been determined. These linear codes contain some…
We consider generalizations of Reed-Muller codes, toric codes, and codes from certain plane curves, such as those defined by norm and trace functions on finite fields. In each case we are interested in codes defined by evaluating arbitrary…
This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…
In this work we study metric properties of the well-known family of binary Reed-Muller codes. Let $A$ be an arbitrary subset of the Boolean cube, and $\widehat{A}$ be the metric complement of $A$ -- the set of all vectors of the Boolean…
A quantum single-error-correcting scheme can be derived from a one-way entanglement purification protocol in purifying one Bell state from a finite block of five Bell states. The main issue to be concerned with in the theory of such an…
Rotation symmetric Boolean functions have important applications in the design of cryptographic algorithms. In this paper, the Conjecture about rotation symmetric Boolean functions (RSBFs) of degree 3 proposed by Cusik and St\u{a}nic\u{a}…
The well known Plotkin construction is, in the current paper, generalized and used to yield new families of Z2Z4-additive codes, whose length, dimension as well as minimum distance are studied. These new constructions enable us to obtain…
The notion of a KU-valued function on a set is introduced and related properties are investigated. Codes generated by KU-valued functions are established. Moreover, we will provide an algorithm which allows us to find a KU-algebra starting…
Plateaued functions as an extension of bent functions play a significant role in cryptography, coding theory, sequences and combinatorics. In \cite{Mesnager9}, Mesnager \emph{et al.} introduced generalized plateaued functions in order to…
Multivariate multiplicity codes (Kopparty, Saraf, and Yekhanin, J. ACM 2014) are linear codes where the codewords are described by evaluations of multivariate polynomials (with a degree bound) and their derivatives up to a fixed order, on a…
This paper is about certain string-to-string functions, called the polyregular functions. These are like the regular string-to-string functions, except that they can have polynomial (and not just linear) growth. The class has four…