Related papers: Submodule codes as spherical codes in buildings
We conjecture an algorithm to construct spin multipartitions and prove that all the level one Fock spaces using our combinatorics are modules over the quantum enveloping algebra.
A complex spherical code is a finite subset on the unit sphere in $\mathbb{C}^d$. A fundamental problem on complex spherical codes is to find upper bounds for those with prescribed inner products. In this paper, we determine the irreducible…
One of the main problems of the research area of network coding is to compute good lower and upper bounds of the achievable cardinality of so-called subspace codes in $\operatorname{PG}(n,q)$, i.e., the set of subspaces of $\mathbb{F}_q^n$,…
Quantum error-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…
We show that ideal submodules and closed ternary ideals in Hilbert modules are the same. We use this insight as a little peg on which to hang a little note about interrelations with other notions regarding Hilbert modules. In Section 3, we…
We develop algorithms to turn quotients of rings of rings of integers into effective Euclidean rings by giving polynomial algorithms for all fundamental ring operations. In addition, we study normal forms for modules over such rings and…
The concept of spatial coupling is among the most significant breakthroughs in coding theory over the past decade. The excellent waterfall and error floor performance of spatially coupled codes has positioned them as promising coding…
Orbit codes are a family of codes employable for communications on a random linear network coding channel. The paper focuses on the classification of these codes. We start by classifying the conjugacy classes of cyclic subgroups of the…
We establish basic results on subrings of finite commutative rings and closely related rings. Among other applications we calculate the number of maximal subrings of a finite commutative local ring.
This work is a survey on completely regular codes. Known properties, relations with other combinatorial structures and constructions are stated. The existence problem is also discussed and known results for some particular cases are…
We describe the structure of bimodules (over finite dimensional algebras) which have the property that the functor of tensoring with such a bimodule sends any module to a projective module. The main result is that all such bimodules are…
We study problems related to indecomposability of modules over certain local finite dimensional trivial extension algebras. We do this by purely combinatorial methods. We introduce the concepts of graph of cyclic modules, of combinatorial…
We set up some basic module theory over semirings, with particular attention to what is needed in scheme theory over semirings. We show that while not all the usual definitions of vector bundle agree over semirings, all the usual…
New exact modular branching rules are obtained for modules over the symmetric groups that are close to completely splittable modules. These results are based on some upper bounds for the Ext^1-spaces between simple modules.
The notions of Betti numbers and of Bass numbers of a finite module N over a local ring R are extended to modules that are only assumed to be finite over S, for some local homomorphism f: R --> S. Various techniques are developed to study…
Combinatorial design theory studies set systems with certain balance and symmetry properties and has applications to computer science and elsewhere. This paper presents a modular approach to formalising designs for the first time using…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, monomials and trinomials over…
Permutation polynomials over finite fields have important applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, etc. In this paper, we construct several new classes of permutation…
Zipper codes are a framework for describing spatially-coupled product-like codes. Many well-known codes, such as staircase codes and braided block codes, are subsumed into this framework. New types of codes such as tiled diagonal and…
Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In…