Related papers: On secret sharing from extended norm-trace curves
Quantum information scrambling has emerged as a powerful tool for studying the dynamics of chaotic quantum many-body systems, assessing benchmarking protocols, and even investigating exotic black hole models. During quantum information…
The generalized Hamming weights of a linear code have been extensively studied since Wei first use them to characterize the cryptography performance of a linear code over the wire-tap channel of type II. In this paper, we investigate the…
In some quantum secret sharing schemes, it is known that some shares can be distributed to participants before a secret is given to the dealer. However, it is unclear whether some shares can be distributed before a secret is given in the…
The generalized Hamming weight of linear codes is a natural generalization of the minimum Hamming distance. They convey the structural information of a linear code and determine its performance in various applications, and have become one…
Shamir's celebrated secret sharing scheme provides an efficient method for encoding a secret of arbitrary length $\ell$ among any $N \leq 2^\ell$ players such that for a threshold parameter $t$, (i) the knowledge of any $t$ shares does not…
We study the properties of secret sharing schemes, where a random secret value is transformed into shares distributed among several participants in such a way that only the qualified groups of participants can recover the secret value. We…
In this paper, we study the hardness of decoding a random code endowed with the cover metric. As the cover metric lies in between the Hamming and rank metric, it presents itself as a promising candidate for code-based cryptography. We give…
This paper is on developing some computer-assisted proof methods involving non-classical inequalities for Shannon entropy. Two areas of the applications of information inequalities are studied: Secret sharing schemes and hat guessing games.…
The decreasing norm-trace codes are evaluation codes defined by a set of monomials closed under divisibility and the rational points of the extended norm-trace curve. In particular, the decreasing norm-trace codes contain the one-point…
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,…
Universal security over a network with linear network coding has been intensively studied. However, previous linear codes and code pairs used for this purpose were linear over a larger field than that used on the network, which restricts…
The sum-rank metric arises as an algebraic approach for coding in MIMO block-fading channels and multishot network coding. Codes designed in the sum-rank metric have raised interest in applications such as streaming codes, robust coded…
The ramp quantum secret sharing proposed by Ogawa et al. has the highest possible coding rate given a threshold type access structure. On the other hand, in some quantum secret sharing schemes, it is known that some shares can be…
We introduce the first geometric construction of codes in the sum-rank metric, which we called linearized Algebraic Geometry codes, using quotients of the ring of Ore polynomials with coefficients in the function field of an algebraic…
Associated to any finite metric space are a large number of objects and quantities which provide some degree of structural or geometric information about the space. In this paper we show that in the setting of subsets of weighted Hamming…
This paper introduces new constructions of sum-rank metric codes derived from algebraic function fields, as existing results on such codes remain limited. A major challenge lies in the determination of their parameters. We address this…
We use the relations between quadrics, trace codes and algebraic curves to construct algebraic curves over finite fields with many points and to compute generalized Hamming weights of codes.
We consider the leakage resilience of AG code-based ramp secret sharing schemes extending the leakage resilience of linear threshold secret sharing schemes over prime fields done by Benhamouda et al. Since there is not any explicit…
Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via a…
In this article, we consider limit theorems for some weighted type random sums (or discrete rough integrals). We introduce a general transfer principle from limit theorems for unweighted sums to limit theorems for weighted sums via rough…