Related papers: A characterization of $\mathbb{Z}_2\mathbb{Z}_2[u]…

For any code loop $L$, we prove that the half-automorphism group of $L$ is the product of the automorphism group of $L$ by an elementary abelian $2-$group consisting of all half-automorphisms that acts as the identity on a fixed basis.…

We prove that the only primes which may divide the order of the automorphism group of a putative binary self-dual doubly-even [120, 60, 24] code are 2, 3, 5, 7, 19, 23 and 29. Furthermore we prove that automorphisms of prime order $p \geq…

Motivated by investigations of rainbow matchings in edge colored graphs, we introduce the notion of color-line graphs that generalizes the classical concept of line graphs in a natural way. Let $H$ be a (properly) edge-colored graph. The…

Delsarte showed that for any projective linear code over a finite field of characteristic p with two nonzero Hamming weights w1 < w2 there exist positive integers u and s such that w1 = (p^s)u and w2 = (p^s)(u+1). Moreover, he showed that…

We show that if we enrich first order logic by allowing quantification over isomorphisms between definable ordered fields the resulting logic, L(Q_{Of}), is fully compact. In this logic, we can give standard compactness proofs of various…

Let $\mathcal{C} = (C_1, C_2, \ldots)$ be a sequence of codes such that each $C_i$ is a linear $[n_i,k_i,d_i]$-code over some fixed finite field $\mathbb{F}$, where $n_i$ is the length of the codewords, $k_i$ is the dimension, and $d_i$ is…

The autocorrelation values of two classes of binary sequences are shown to be good in [6]. We study the 2-adic complexity of these sequences. Our results show that the 2-adic complexity of such sequences is large enough to resist the attack…

We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…

Self-dual codes over finite fields and over some finite rings have been of interest and extensively studied due to their nice algebraic structures and wide applications. Recently, characterization and enumeration of Euclidean self-dual…

In this paper we classify all finite 2-groups of class 2 for which every automorphism of order 2 leaving the Frattini subgroup elementwise fixed is inner. We prove that every such group G is isomorphic to Q(n; r) = <a, b| a^{2n}= b^{2r}= 1;…

We give constructions of self-dual and formally self-dual codes from group rings where the ring is a finite commutative Frobenius ring. We improve the existing construction given in \cite{Hurley1} by showing that one of the conditions given…

A finite group is said to have "perfect order classes" if the number of elements of any given order is either zero or a divisor of the order of the group. The purpose of this note is to describe explicitly the finite Hamiltonian groups with…

We determine the automorphism group of Gabidulin codes of full length and characterise when these codes are equivalent to self-dual codes.

Group codes are right or left ideals in a group algebra of a finite group over a finite field. Following ideas of Bazzi and Mitter on group codes over the binary field, we prove that group codes over finite fields of any characteristic are…

Linear codes are considered over the ring $\mathbb{Z}_4+v\mathbb{Z}_4$, where $v^2=v$. Gray weight, Gray maps for linear codes are defined and MacWilliams identity for the Gray weight enumerator is given. Self-dual codes, construction of…

We give a complete characterization of simple graphs whose adjacency matrices generate binary linear complementary dual (LCD) codes. In particular, we completely characterize a distance-regular graph which yields an LCD code in terms of the…

We study the following one-dimensional cubic nonlinear Schr\"{o}dinger system: \[ u_i''+2\Big(\sum_{k=1}^Nu_k^2\Big)u_i=-\mu_iu_i \ \,\ \mbox{in}\, \ \mathbb{R} , \ \ i=1, 2, \cdots, N, \] where $\mu_1\leq\mu_2\leq\cdots\leq\mu_N<0$ and…

In this paper, we study the wireline two-unicast-Z communication network over directed acyclic graphs. The two-unicast-Z network is a two-unicast network where the destination intending to decode the second message has apriori side…

We present some basic theory on the duality of codes over two non-unital rings of order $6$, namely $H_{23}$ and $H_{32}$. For a code $\mathcal{C}$ over these rings, we associate a binary code $\mathcal{C}_a$ and a ternary code…

Let $\mathbb{F}_{2^m}$ be a finite field of cardinality $2^m$, $\lambda$ and $k$ be integers satisfying $\lambda,k\geq 2$ and denote $R=\mathbb{F}_{2^m}[u]/\langle u^{2\lambda}\rangle$. Let $\delta,\alpha\in \mathbb{F}_{2^m}^{\times}$. For…