Related papers: A ternary construction of lattices
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…
We give a new algorithm to construct optimal alphabetic ternary trees, where every internal node has at most three children. This algorithm generalizes the classic Hu-Tucker algorithm, though the overall computational complexity has yet to…
Polar code lattices are formed from binary polar codes using Construction D. In this paper, we propose a design technique for finite-dimension polar code lattices. The dimension $n$ and target probability of decoding error are parameters…
For lengths $36$, $48$ and $60$, we construct new ternary near-extremal self-dual codes with weight enumerators for which no ternary near-extremal self-dual codes were previously known to exist.
Most multi-dimensional (more than two dimensions) lattice partitions only form additive quotient groups and lack multiplication operations. This prevents us from constructing lattice codes based on multi-dimensional lattice partitions…
In this article, we study new methods for constructing uninorms on bounded lattices. First, we present new methods for constructing uninorms on bounded lattices under the additional constraints and prove that some of these constraints are…
In this paper, we will give the generic construction of a binary linear code of dimension $n+3$ and derive the necessary and sufficient conditions for the constructed code to be minimal. Using generic construction, a new family of minimal…
The construction of deletion codes for the Levenshtein metric is reduced to the construction of codes over the integers for the Manhattan metric by run length coding. The latter codes are constructed by expurgation of translates of…
We construct a family of linear maximally recoverable codes with locality $r$ and dimension $r+1.$ For codes of length $n$ with $r\approx n^\alpha, 0\le\alpha\le 1$ the code alphabet is of the order $n^{1+3\alpha},$ which improves upon the…
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…
In this paper we give the generalization of lifted codes over any finite chain ring. This has been done by using the construction of finite chain rings from $p$-adic fields. Further we propose a lattice construction from linear codes over…
Recently, linear codes constructed by defining sets have attracted a lot of study, and many optimal linear codes with a few weights have been produced. The objective of this paper is to present a class of binary linear codes with three…
New $s$-extremal extremal unimodular lattices in dimensions $38$, $40$, $42$ and $44$ are constructed from self-dual codes over $\mathbb{F}_5$ by Construction A. In the process of constructing these codes, we obtain a self-dual $[44,22,14]$…
Low density generator matrix (LDGM) codes have an acceptable performance under iterative decoding algorithms. This idea is used to construct a class of lattices with relatively good performance and low encoding and decoding complexity. To…
The so-called min-sum algorithm has been applied for decoding lattices constructed by Construction D'. We generalize this iterative decoding algorithm to decode lattices constructed by Construction D. An upper bound on the decoding…
We characterize all residuated lattices that have height equal to $3$ and show that the variety they generate has continuum-many subvarieties. More generally, we study unilinear residuated lattices: their lattice is a union of disjoint…
We investigate a construction of an integral residuated lattice starting from an integral residuated lattice and two sets with an injective mapping from one set into the second one. The resulting algebra has a shape of a Chinese cascade…
We present an improved orderly algorithm for constructing all unlabelled lattices up to a given size, that is, an algorithm that constructs the minimal element of each isomorphism class relative to some total order. Our algorithm employs a…
We construct vertex transitive lattices on products of trees of arbitrary dimension $d \geq 1$ based on quaternion algebras over global fields with exactly two ramified places. Starting from arithmetic examples, we find non-residually…
Any simple Lie superalgebras over the complex field can be constructed from some triple systems. Examples of Lie superalgebras $D(2,1;\alpha)$, G(3) and F(4) are given by utilizing a general construction method based upon $(-1,-1)$ balanced…