Related papers: A Construction of Binary Linear Codes from Boolean…
The two-terminal key agreement problem with biometric or physical identifiers is considered. Two linear code constructions based on Wyner-Ziv coding are developed. The first construction uses random linear codes and achieves all points of…
Linear codes with few weights have significant applications in secret sharing schemes, authentication codes, association schemes, and strongly regular graphs. There are a number of methods to construct linear codes, one of which is based on…
Minimal linear codes have significant applications in secret sharing schemes and secure two-party computation. There are several methods to construct linear codes, one of which is based on functions over finite fields. Recently, many…
In this work we cast the problem of binary classification in terms of estimating a partition on Bernoulli data. When the explanatory variables are all categorical, the problem can be modelled using the language of boolean functions. We…
Boolean functions are mathematical objects with numerous applications in domains like coding theory, cryptography, and telecommunications. Finding Boolean functions with specific properties is a complex combinatorial optimization problem…
It is proved an amplification of Cusick-Cheon's conjecture on balanced Boolean functions in the cosets of the binary Reed-Muller code RM(k,m) of order k and length 2^m, in the cases where k = 1 or k >= (m-1)/2.
Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iterative message passing. Concepts from mathematical…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, almost perfect nonlinear…
Boolean function bi-decomposition is ubiquitous in logic synthesis. It entails the decomposition of a Boolean function using two-input simple logic gates. Existing solutions for bi-decomposition are often based on BDDs and, more recently,…
Long linear codes constructed from toric varieties over finite fields, their multiplicative structure and decoding. The main theme is the inherent multiplicative structure on toric codes. The multiplicative structure allows for…
Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary construction of linear codes based on their weight…
Linear codes with a few weights can be applied to communication, consumer electronics and data storage system. In addition, the weight hierarchy of linear codes has many applications such as on the type II wire-tap channel, dealing with…
Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms. They have been studied for decades and a lot of progress has been made.…
In this paper, we apply two-to-one functions over $\mathbb{F}_{2^n}$ in two generic constructions of binary linear codes. We consider two-to-one functions in two forms: (1) generalized quadratic functions; and (2) $\left(x^{2^t}+x\right)^e$…
In [2] we show how to construct information sets for Reed-Muller codes only in terms of their basic parameters. In this work we deal with the corresponding problem for q-ary Generalized Reed-Muller codes of first and second order. We see…
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…
We give a description of the duals of linearized Reed-Solomon codes in terms of codes obtained by taking residues of Ore rational functions. Our construction shows in particular that, under some assumptions on the base field, the class of…
Linear codes with few weights have many applications in secret sharing schemes, authentication codes, communication and strongly regular graphs. In this paper, we consider linear codes with three weights in arbitrary characteristic. To do…
We define and study a class of Reed-Muller type error-correcting codes obtained from elementary symmetric functions in finitely many variables. We determine the code parameters and higher weight spectra in the simplest cases.
In this paper, we mainly investigate profound interconnections between combinatorial designs, linear codes, and Boolean functions.