Related papers: Linear codes associated with the Desarguesian ovoi…
It is shown in this paper that, if $R$ is a Frobenius ring, then the quaternion ring $\mathcal{H}_{a,b}(R)$ is a Frobenius ring for all units $a,b \in R$. In particular, if $q$ is an odd prime power then $\mathcal{H}_{a,b}(\mathbb{F}_q)$ is…
Let $(V,q)$ be a non-degenerate $n$-dimensional quadratic space over the rationals of real signature $(r,s)$. For every integer $1\leq k \leq \min\{r,n-2\}$ we construct classes in the cohomology of arithmetic subgroups of $\mathrm{O}(V)$…
Let A_{R,q} denote a family of covering codes, in which the covering radius R and the size q of the underlying Galois field are fixed, while the code length tends to infinity. In this paper, infinite sets of families A_{R,q}, where R is…
We describe a successive-cancellation \emph{list} decoder for polar codes, which is a generalization of the classic successive-cancellation decoder of Ar{\i}kan. In the proposed list decoder, up to $L$ decoding paths are considered…
The setting of projective systems can be used to study the parameters of a projective linear code $\mathcal{C}$. This can be done by considering the intersections of the point set $\Omega$ defined by the columns of a generating matrix for…
"Extended Clifford algebras" are introduced as a means to obtain low ML decoding complexity space-time block codes. Using left regular matrix representations of two specific classes of extended Clifford algebras, two systematic algebraic…
Let $\FRAK{g}$ be a classical simple Lie superalgebra. To every nilpotent orbit $\cal O$ in $\FRAK{g}_0$ we associate a Clifford algebra over the field of rational functions on $\cal O$. We find the rank, $k(\cal O)$ of the bilinear form…
Let $V(\lambda)$ be the irreducible lowest weight $U_q(D(N,1))$-module with lowest weight $\lambda$. Assume $\lambda = n_0\omega_0-\sum_{i=0}^{N}n_i\omega_i$, where $\omega_0$ is the fundamental weight corresponding to the unique odd coroot…
Self-dual binary linear codes have been extensively studied and classified for length n <= 40. However, little attention has been paid to linear codes that coincide with their orthogonal complement when the underlying inner product is not…
The length function $\ell_q(r,R)$ is the smallest possible length $n$ of a $ q $-ary linear $[n,n-r]_qR$ code with codimension (redundancy) $r$ and covering radius $R$. Let $s_q(N,\rho)$ be the smallest size of a $\rho$-saturating set in…
Recently, linear codes with a few weights were widely investigated due to their applications in secret sharing schemes and authentication schemes. In this letter, we present a class of $q$-ary linear codes derived from irreducible cyclic…
A class of optimal three-weight cyclic codes of dimension 3 over any finite field was presented by Vega [Finite Fields Appl., 42 (2016) 23-38]. Shortly thereafter, Heng and Yue [IEEE Trans. Inf. Theory, 62(8) (2016) 4501-4513] generalized…
In this article we provide simple and provable bounds on the size and shape of the locus of discrete subgroups of $\mathsf{PSL}(2,\mathbb{C})\cong \operatorname{Isom}^+(\mathbb{H}^3)$ which split as a free product of cyclic groups…
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…
It is well known that a random q-ary code of rate \Omega(\epsilon^2) is list decodable up to radius (1 - 1/q - \epsilon) with list sizes on the order of 1/\epsilon^2, with probability 1 - o(1). However, until recently, a similar statement…
The Veldkamp space, in the sense of Buekenhout and Cohen, of the generalized quadrangle GQ(4, 2) is shown not to be a (partial) linear space by simply giving several examples of Veldkamp lines (V-lines) having two or even three Veldkamp…
In this paper we construct functional codes from Denniston maximal arcs. For $q=2^{4n+2}$ we obtain linear codes with parameters $[(\sqrt{q}-1)(q+1),5,d]_q$ where $\lim_{q \to +\infty} d=(\sqrt{q}-1)q-3\sqrt{q}$. We also find for $q=16,32$…
Let $\mathcal{O}_c$ be the category of finite-length modules for the Virasoro Lie algebra at central charge $c$ whose composition factors are irreducible quotients of reducible Verma modules. For any $c\in\mathbb{C}$, this category admits…
Motivated by recent neutron, X-ray absorption and resonant scattering experiments, we revisit the electronic structure of V2O3. We propose a model in which S=1 V3+ ions are coupled in the vertical V-V pairs forming two-fold orbitally…
Under a suitable hypothesis, we construct a full set of pairwise orthogonal maximal vectors in $V^{\otimes n}$, where $V=V(1)$ is the simple module of highest weight $1$ for the quantized enveloping algebra $\mathbf{U}(\mathfrak{sl}_2)$. We…