Related papers: On the Locality of Codeword Symbols in Non-Linear …
Most bounds on the size of codes hold for any code, whether linear or not. Notably, the Griesmer bound holds only in the linear case and so optimal linear codes are not necessarily optimal codes. In this paper we identify code parameters…
The principle of non-violation of "information causality", has been proposed as one of the foundational properties of nature\cite{nature}. The main goal of the paper is to explore the gap between quantum mechanical correlations and those…
We show that in principle, $N$-partite unitary transformations can be perfectly discriminated under local measurement and classical communication (LOCC) despite of their nonlocal properties. Based on this result, some related topics,…
We investigate the stopping redundancy hierarchy of linear block codes and its connection to permutation decoding techniques. An element in the ordered list of stopping redundancy values represents the smallest number of possibly linearly…
We present a theoretical framework that extends classical information theory to finite and structured systems by redefining redundancy as a fundamental property of information organization rather than inefficiency. In this framework,…
We adapt the method of solution regions to prove new existence and localization results for systems of discontinuous differential equations. Some assumptions concerning the definition of a solution region are relaxed and thus our results…
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…
Nonlocality exhibited by ensembles of composite quantum states, wherein local operations and classical communication (LOCC) yield suboptimal discrimination probabilities compared to global strategies, is one of the striking nonclassical…
We construct new linear codes with high minimum distance d. In at least 12 cases these codes improve the minimum distance of the previously known best linear codes for fixed parameters n,k. Among these new codes there is an optimal ternary…
Optimal prefix codes are studied for pairs of independent, integer-valued symbols emitted by a source with a geometric probability distribution of parameter $q$, $0{<}q{<}1$. By encoding pairs of symbols, it is possible to reduce the…
The objective of this paper is to construct a class of linear codes with two nonzero weights and three nonzero weights by using the general trace functions, which weight distributions has been determined. These linear codes contain some…
In this paper we study two different ways of coupling a local operator with a nonlocal one in such a way that the resulting equation is related to an energy functional. In the first strategy the coupling is given via source terms in the…
The $q$-ary block codes with two distances $d$ and $d+1$ are considered. Several constructions of such codes are given, as in the linear case all codes can be obtained by a simple modification of linear equidistant codes. Upper bounds for…
This study addresses the use of Reed-Solomon error correction codes in QR codes to enhance resilience against failures. To fully grasp this approach, a basic cryptographic context is provided, necessary for understanding Reed-Solomon codes.…
Bell nonlocality can be formulated in terms of a resource theory with local-hidden variable models as resourceless objects. Two such theories are known, one built upon local operations assisted by shared randomness (LOSRs) and the other one…
We show that loop quantum gravity suffers from a potential problem with non-locality, coming from a mismatch between micro-locality, as defined by the combinatorial structures of their microscopic states, and macro-locality, defined by the…
A code over a finite alphabet is called locally recoverable (LRC code) if every symbol in the encoding is a function of a small number (at most $r$) other symbols of the codeword. In this paper we introduce a construction of LRC codes on…
Index coding achieves bandwidth savings by jointly encoding the messages demanded by all the clients in a broadcast channel. The encoding is performed in such a way that each client can retrieve its demanded message from its side…
Reed-Muller codes are among the most important classes of locally correctable codes. Currently local decoding of Reed-Muller codes is based on decoding on lines or quadratic curves to recover one single coordinate. To recover multiple…
This paper presents new lower and upper bounds for the optimal compression of binary prefix codes in terms of the most probable input symbol, where compression efficiency is determined by the nonlinear codeword length objective of…