Related papers: LCPs of Subspace Codes
We call a linear code $C$ with length $n$ over a field $F$, a linear complementary equi-dual code, when there exists a linear code $D$ over $F$ such that $D$ is permutation equivalent to $C^\perp$ and $(C,D)$ is a linear complementary pair…
This paper is concerned with linear superposition systems in which all components of the superimposed signal are coded with an identical binary low-density parity-check (LDPC) code.
Linear complementary dual (LCD) codes and linear complementary pair (LCP) of codes over finite fields have been intensively studied recently due to their applications in cryptography, in the context of side-channel and fault injection…
Due to their widespread applications, linear complementary pairs (LCPs) have attracted much attention in recent years. In this paper, we determine explicit construction of non-special divisors of degree $g$ and $g-1$ on Kummer extensions…
A pair $(C, D)$ of group codes over group algebra $R[G]$ is called a linear complementary pair (LCP) if $C \oplus D =R[G]$, where $R$ is a finite principal ideal ring, and $G$ is a finite group. We provide a necessary and sufficient…
Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings $R_k$.…
We provide a novel framework to study subspace codes for non-coherent communications in wireless networks. To this end, an analog operator channel is defined with inputs and outputs being subspaces of $\mathbb{C}^n$. Then a certain distance…
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…
In this paper, on one hand, a class of linear codes with one or two weights is obtained. Based on these linear codes, we construct two classes of constant composition codes, which includes optimal constant composition codes depending on…
Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. We give a characterization of LCD codes over $\mathbb{F}_q$ having large minimum weights for $q \in \{2,3\}$. Using the characterization, we…
The surface code is a two-dimensional topological code with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet…
LCD codes are linear codes that intersect with their dual trivially. Quasi cyclic codes that are LCD are characterized and studied by using their concatenated structure. Some asymptotic results are derived. Hermitian LCD codes are…
Given a finite field F_q and a positive integer n, a flag is a sequence of nested F_q-subspaces of a vector space F_q^n and a flag code is a nonempty collection of flags. The projected codes of a flag code are the constant dimension codes…
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…
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 main goal of coding theory is to devise efficient systems to exploit the full capacity of a communication channel, thus achieving an arbitrarily small error probability. Low Density Parity Check (LDPC) codes are a family of block…
Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to their practical applications in computational complexity and information…
The set of all subspaces of $\mathbb{F}_q^n$ is denoted by $\mathbb{P}_q(n)$. The subspace distance $d_S(X,Y) = \dim(X)+ \dim(Y) - 2\dim(X \cap Y)$ defined on $\mathbb{P}_q(n)$ turns it into a natural coding space for error correction in…
We discuss how subspace codes can be used to simultaneously correct errors and erasures when the network performs random linear network coding and the edges are noisy channels. This is done by combining the subspace code with a classical…
In the context of constant--dimension subspace codes, an important problem is to determine the largest possible size $A_q(n, d; k)$ of codes whose codewords are $k$-subspaces of $\mathbb{F}_q^n$ with minimum subspace distance $d$. Here in…