Related papers: Secret sharing with a class of minimal linear code…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
Nested code pairs play a crucial role in the construction of ramp secret sharing schemes [Kurihara et al. 2012] and in the CSS construction of quantum codes [Ketkar et al. 2006]. The important parameters are (1) the codimension, (2) the…
Linear intersection pairs of linear codes have become of interest due to their nice algebraic properties and wide applications. In this paper, we focus on linear intersection pairs of cyclic codes over finite fields. Some properties of…
Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In…
Coded caching systems have been widely studied to reduce the data transmission during the peak traffic time. In practice, two important parameters of a coded caching system should be considered, i.e., the rate which is the maximum amount of…
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…
In this paper, based on the theory of defining sets, two classes of at most six-weight linear codes over $\mathbb{F}_p$ are constructed. The weight distributions of the linear codes are determined by means of Gaussian period and Weil sums.…
Ramp secret sharing (SS) schemes can be classified into strong ramp SS schemes and weak ramp SS schemes. The strong ramp SS schemes do not leak out any part of a secret explicitly even in the case where some information about the secret…
Hinging on ideas from physical-layer network coding, some promising proposals of coded random access systems seek to improve system performance (while preserving low complexity) by means of packet repetitions and decoding of linear…
Recent sequential pattern mining methods have used the minimum description length (MDL) principle to define an encoding scheme which describes an algorithm for mining the most compressing patterns in a database. We present a novel…
Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties so that certain subsets can reconstruct the secret, while unauthorized subsets obtain no information. While QSS was introduced over…
We study the arithmetic circuit complexity of threshold secret sharing schemes by characterizing the graph-theoretic properties of arithmetic circuits that compute the shares. Using information inequalities, we prove that any unrestricted…
New lower bounds on the minimum average Hamming distance of binary codes are derived. The bounds are obtained using linear programming approach.
Relative generalized Hamming weights (RGHWs) of a linear code respect to a linear subcode determine the security of the linear ramp secret sharing scheme based on the code. They can be used to express the information leakage of the secret…
In this paper, we first study in detail the relationship between minimal linear codes and cutting blocking sets, which were recently introduced by Bonini and Borello, and then completely characterize minimal linear codes as cutting blocking…
A general lossless joint source-channel coding scheme based on linear codes is proposed and then analyzed in this paper. It is shown that a linear code with good joint spectrum can be used to establish limit-approaching joint source-channel…
Dihedral codes, particular cases of quasi-cyclic codes, have a nice algebraic structure which allows to store them efficiently. In this paper, we investigate it and prove some lower bounds on their dimension and minimum distance, in analogy…
Random linear network codes can be designed and implemented in a distributed manner, with low computational complexity. However, these codes are classically implemented over finite fields whose size depends on some global network parameters…
We study the communication efficient secret sharing (CESS) problem introduced by Huang, Langberg, Kliewer and Bruck. A classical threshold secret sharing scheme randomly encodes a secret into $n$ shares given to $n$ parties, such that any…
Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…