Related papers: Conjugate Codes and Applications to Cryptography
We introduce {\bf complementary information set codes} of higher-order. A binary linear code of length $tk$ and dimension $k$ is called a complementary information set code of order $t$ ($t$-CIS code for short) if it has $t$ pairwise…
We introduce the concept of a Girard couple, which consists of two (not necessarily unital) quantales linked by a strong form of duality. The two basic examples of Girard couples arise in the study of endomorphism quantales and of the…
Two new constructions of linear code pairs $C_2 \subset C_1$ are given for which the codimension and the relative minimum distances $M_1(C_1,C_2)$, $M_1(C_2^\perp,C_1^\perp)$ are good. By this we mean that for any two out of the three…
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…
Symmetry is at the heart of coding theory. Codes with symmetry, especially cyclic codes, play an essential role in both theory and practical applications of classical error-correcting codes. Here we examine symmetry properties for codeword…
Cryptography literally means "The art & science of secret writing & sending a message between two parties in such a way that its contents cannot be understood by someone other than the intended recipient". and Quantum word is related with…
Several pairing-based cryptographic protocols are recently proposed with a wide variety of new novel applications including the ones in emerging technologies like cloud computing, internet of things (IoT), e-health systems and wearable…
Linear complementary pairs (LCPs) of codes have been studied since they were introduced in the context of discussing mitigation measures against possible hardware attacks to integrated circuits. In this situation, the security parameters…
We introduce a new tool for the study of isogeny-based cryptography, namely pairings which are sesquilinear (conjugate linear) with respect to the $\mathcal{O}$-module structure of an elliptic curve with CM by an imaginary quadratic order…
Symbol-pair code is a new coding framework which is proposed to correct errors in the symbol-pair read channel. In particular, maximum distance separable (MDS) symbol-pair codes are a kind of symbol-pair codes with the best possible…
Asymmetric quantum error-correcting codes are quantum codes defined over biased quantum channels: qubit-flip and phase-shift errors may have equal or different probabilities. The code construction is the Calderbank-Shor-Steane construction…
The data transmission protocol, based on the use of a strongly correlated pair of laser beams, is proposed. The properties of the corresponding states are described in detail. The protocol is based on the strong correlation of photon…
Classical symmetric pairs consist of a symmetrizable Kac-Moody algebra $\mathfrak{g}$, together with its subalgebra of fixed points under an involutive automorphism of the second kind. Quantum group analogs of this construction, known as…
Split Cooper pair is a natural source for entangled electrons which is a basic ingredient for quantum information in solid state. We report an experiment on a superconductor-graphene double quantum dot (QD) system, in which we observe…
Networks of chaotic coupled maps are considered as string and language generators. It is shown that such networks can be used as encrypting systems where the ciphertext contains information about the evolution of the network and also about…
The notion of 'presentation', as used in combinatorial group theory, is applied to coded character sets(CCSs) - sets which facilitate the interchange of messages in a digital computer network(DCN) . By grouping each element of the set into…
This paper investigates the concept of self-dual convolutional code. We derive the basic properties of this interesting class of codes and we show how some of the techniques to construct self-dual linear block codes generalize to self-dual…
Network coding is a technique to maximize communication rates within a network, in communication protocols for simultaneous multi-party transmission of information. Linear network codes are examples of such protocols in which the local…
In this paper, we highlight the class of spatially coupled codes and discuss their applicability to long-haul and submarine optical communication systems. We first demonstrate how to optimize irregular spatially coupled LDPC codes for their…
A general class of authentication schemes for arbitrary quantum messages is proposed. The class is based on the use of sets of unitary quantum operations in both transmission and reception, and on appending a quantum tag to the quantum…