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For a finite separable field extension K/k, all subfields can be obtained by intersecting so-called principal subfields of K/k. In this work we present a way to quickly compute these intersections. If the number of subfields is high, then…
Private information retrieval (PIR) considers the problem of retrieving a data item from a database or distributed storage system without disclosing any information about which data item was retrieved. Secure PIR complements this problem by…
Traditional algebraic geometric invariants lose some of their potency in positive characteristic. For instance, smooth projective hypersurfaces may be covered by lines despite being of arbitrarily high degree. The purpose of this…
In this article we mainly study linear codes over $\mathbb{F}_{2^n}$ and their binary subfield codes. We construct linear codes over $\mathbb{F}_{2^n}$ whose defining sets are the certain subsets of $\mathbb{F}_{2^n}^m$ obtained from…
We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ with symmetric generator matrices from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$. Using this method, we improve the…
In this paper we introduce and investigate rank-metric intersecting codes, a new class of linear codes in the rank-metric context, inspired by the well-studied notion of intersecting codes in the Hamming metric. A rank-metric code is said…
High-rate quantum error correcting codes mitigate the imposing scale of fault-tolerant quantum computers but require efficient generation of non-local, many-body entanglement. We provide a linear-optical architecture with these properties,…
Secure codes are widely-studied combinatorial structures which were introduced for traitor tracing in broadcast encryption. To determine the maximum size of such structures is the main research objective. In this paper, we investigate the…
Multi-secret sharing is an extension of secret sharing technique where several secrets are shared between the participants, each according to a specified access structure. The secrets can be reconstructed according to the access structure…
Linear codes with few weights have applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, several classes of two-weight and three-weight linear codes are presented and their…
We consider the question of determining the maximum number of $\mathbb{F}_q$-rational points that can lie on a hypersurface of a given degree in a weighted projective space over the finite field $\mathbb{F}_q$, or in other words, the…
We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of…
Secret sharing schemes based on the idea of hidden multipliers in encryption are proposed. As a platform, one can use both multiplicative groups of finite fields and groups of invertible elements of commutative rings, in particular,…
We propose an adaptive threshold multi secret sharing scheme based solely on cryptographically secure hash functions. We show that the proposed scheme is also: perfect, ideal, verifiable, and proactive. Moreover the proposed scheme has a…
In this paper, we propose a class of threshold secret sharing schemes with repairing function between shares without the help of the dealer, that we called repairable threshold secret sharing schemes. Specifically, if a share fails, such as…
We propose a new low-density parity-check code construction scheme based on 2-lifts. The proposed codes have an advantage of admitting efficient hardware implementations. With the motivation of designing codes with low error floors, we…
Topological subsystem codes can combine the advantages of both topological codes and subsystem codes. Suchara et al. proposed a framework based on hypergraphs for construction of such codes. They also studied the performance of some…
We propose a family of surface codes with general lattice structures, where the error-tolerances against bit and phase errors can be controlled asymmetrically by changing the underlying lattice geometries. The surface codes on various…
Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. Subsystem codes generalize all major quantum error protection schemes, and therefore are especially versatile. This…
The computational cost of micromechanics for heterogeneous materials can be reduced in certain cases where symmetric boundary conditions are applicable. We derived an eighth symmetric formulation of the Generalized Method of Cells for…