相关论文: Self-dual Codes over the Kleinian Four Group
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 existence and construction of self-dual codes in a permutation module of a finite group for the semisimple case are described from two aspects, one is from the point of view of the composition factors which are self-dual modules, the…
Let $\mathbb{F}_{q}$ be the finite field of $q$ elements and let $D_{2n}=\langle x,y\mid x^n=1, y^2=1, yxy=x^{n-1}\rangle$ be the dihedral group of order $n$. Left ideals of the group algebra $\mathbb{F}_{q}[D_{2n}]$ are known as left…
Starting from a generalization of a recent result on self-duality we systematically analyze self-dual models. We find a criterion to judge whether a given model is self-dual or not. With this tool we construct some new self-dual pairs,…
In the present article we discuss the classification of quantum groups whose quasi-classical limit is a given simple complex Lie algebra $\mathfrak{g}$. This problem reduces to the classification of all Lie bialgebra structures on…
A linear code is said to be self-orthogonal if it is contained in its dual. Self-orthogonal codes are of interest because of their important applications, such as for constructing linear complementary dual (LCD) codes and quantum codes. In…
A linear code is linear complementary dual (LCD) if it meets its dual trivially. LCD codes have been a hot topic recently due to Boolean masking application in the security of embarked electronics (Carlet and Guilley, 2014). Additive codes…
We show how to obtain the dual of any lattice model with inhomogeneous local interactions based on an arbitrary Abelian group in any dimension and on lattices with arbitrary topology. It is shown that in general the dual theory contains…
A Klein surface is a surface with a dianalytic structure. A double of a Klein surface $X$ is a Klein surface $Y$ such that there is a degree two morphism (of Klein surfaces) $Y\rightarrow X$. There are many doubles of a given Klein surface…
The self-dual spaces of polynomials are related to Bethe vectors in the Gaudin model associated to the Lie algebras of types B and C. In this paper, we give lower bounds for the numbers of real self-dual spaces in intersections of Schubert…
In the present paper, we give Assmus--Mattson type theorems for codes and lattices. We show that a binary doubly even self-dual code of length 24m with minimum weight 4m provides a combinatorial 1-design and an even unimodular lattice of…
We consider $d$-dimensional lattice polytopes $\Delta$ with $h^*$-polynomial $h^*_\Delta=1+h_k^*t^k$ for $1<k<(d+1)/2$ and relate them to some abelian subgroups of $\SL_{d+1}(\C)$ of order $1+h_k^*=p^r$ where $p$ is a prime number. These…
We discuss $\mathcal{N}=1$ Klein and Klein-Conformal superspaces in $D=(2,2)$ space-time dimensions, realizing them in terms of their functor of points over the split composition algebra $\mathbb{C}_{s}$. We exploit the observation that…
Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual. Numerical…
We study additive quaternary codes whose parameters are close to those of the extended cyclic [12; 6; 6]4-code or to the quaternary linear codes generated by the elliptic quadric in PG(3; 4) or its dual. In particular we characterize those…
The main theorem in this paper is a far-reaching generalization of Gleason's theorem on the weight enumerators of codes which applies to arbitrary-genus weight enumerators of self-dual codes defined over a large class of finite rings and…
Given a finite extension $K/F$ of degree $r$ of a finite field $F$, we enumerate all selfdual skew cyclic codes in the Ore quotient ring $K[X;\text{Frob}]/(X^{rk}-1)$ for any positive integer $k$ coprime to the characteristic $p$ (separable…
In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions when this construction can yield self-dual codes. We construct…
Linear codes with complementary duals are linear codes whose intersection with their duals are trivial, shortly named LCD codes. In this paper we outline a construction for LCD codes over finite fields of order $q$ using weighing matrices…
There is a rich connection between classical error-correcting codes, Euclidean lattices, and chiral conformal field theories. Here we show that quantum error-correcting codes, those of the stabilizer type, are related to Lorentzian lattices…