Related papers: Secret sharing with a class of minimal linear code…
Linear codes have been an interesting topic in both theory and practice for many years. In this paper, a class of $q$-ary linear codes with few weights are presented and their weight distributions are determined using Gauss periods. Some 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…
Secret sharing schemes with optimal and universal communication overheads have been obtained independently by Bitar et al. and Huang et al. However, their constructions require a finite field of size q > n, where n is the number of shares,…
Privacy-preserving machine learning is learning from sensitive datasets that are typically distributed across multiple data owners. Private machine learning is a remarkable challenge in a large number of realistic scenarios where no trusted…
Minimal codewords have applications in decoding linear codes and in cryptography. We study the number of minimal codewords in binary linear codes that arise by appending a unit matrix to the adjacency matrix of a graph.
A secret sharing scheme (SSS) was introduced by Shamir in 1979 using polynomial interpolation. Later it turned out that it is equivalent to an SSS based on a Reed-Solomon code. SSSs based on linear codes have been studied by many…
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…
In the paper we discuss how to share the secrets, that are graphs. So, far secret sharing schemes were designed to work with numbers. As the first step, we propose conditions for "graph to number" conversion methods. Hence, the existing…
Linear codes with a few weights have many nice applications including combinatorial design, distributed storage system, secret sharing schemes and so on. In this paper, we construct two families of linear codes with a few weights based on…
A secret sharing scheme is a cryptographic protocol to distribute a secret state in an encoded form among a group of players such that only authorized subsets of the players can reconstruct the secret. Classically, efficient secret sharing…
This work investigates the design of sparse secret sharing schemes that encode a sparse private matrix into sparse shares. This investigation is motivated by distributed computing, where the multiplication of sparse and private matrices is…
We consider a coded cooperative data exchange problem with the goal of generating a secret key. Specifically, we investigate the number of public transmissions required for a set of clients to agree on a secret key with probability one,…
Given a real dataset and a computation family, we wish to encode and store the dataset in a distributed system so that any computation from the family can be performed by accessing a small number of nodes. In this work, we focus on the…
Boolean functions have very nice applications in cryptography and coding theory, which have led to a lot of research focusing on their applications. The objective of this paper is to construct binary linear codes with few weights from the…
Any secured system can be modeled as a capability-based access control system in which each user is given a set of secret keys of the resources he is granted access to. In some large systems with resource-constrained devices, such as sensor…
Linear codes have been an interesting subject of study for many years, as linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a class of…
Bipartite secret sharing schemes have a bipartite access structure in which the set of participants is divided into two parts and all participants in the same part play an equivalent role. Such a bipartite scheme can be described by a…
Secret sharing provides a means to distribute shares of a secret such that any authorized subset of shares, specified by an access structure, can be pooled together to recompute the secret. The standard secret sharing model requires public…
In this paper we investigate the use of quantum information to share classical secrets. While every quantum secret sharing scheme is a quantum error correcting code, the converse is not true. Motivated by this we sought to find quantum…
The square $C^{*2}$ of a linear error correcting code $C$ is the linear code spanned by the component-wise products of every pair of (non-necessarily distinct) words in $C$. Squares of codes have gained attention for several applications…