Related papers: An inductive construction of minimal codes
We develop three approaches of combinatorial flavour to study the structure of minimal codes and cutting blocking sets in finite geometry, each of which has a particular application. The first approach uses techniques from algebraic…
The goal of this article is to exhibit two new families of finitely generated simple groups of homeomorphisms of $\mathbf{R}$. These families are strikingly different from existing families owing to the nature of their actions on…
We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and…
Creating a new Ontology: a Modular Approach
A finitely generated commutative monoid is uniquely presented if it has only a minimal presentation. We give necessary and sufficient conditions for finitely generated, combinatorially finite, cancellative, commutative monoids to be…
In this paper, we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields and then apply them to construct LCD codes. Construction…
For $n$ and $k$ integers we introduce the notion of some partition of $n$ being able to generate another partition of $n$. We solve the problem of finding the minimum size partition for which the set of partitions this partition can…
Linear codes are the most important family of codes in cryptography and coding theory. Some codes have only a few weights and are widely used in many areas, such as authentication codes, secret sharing schemes and strongly regular graphs.…
One of the main weakness of the family of centralizer codes is that its length is always $n^2$. Thus we have taken a new matrix equation code called intertwining code. Specialty of this code is the length of it, which is of the form $nk$.…
Thin sums matroids were introduced to extend the notion of representability to non-finitary matroids. We give a new criterion for testing when the thin sums construction gives a matroid. We show that thin sums matroids over thin families…
This paper is concerned with the affine-invariant ternary codes which are defined by Hermitian functions. We compute the incidence matrices of 2-designs that are supported by the minimum weight codewords of these ternary codes. The linear…
A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…
In this paper we show how to construct new convolutional codes from old ones by applying the well-known techniques: puncturing, extending, expanding, direct sum, the (u|u + v) construction and the product code construction. By applying…
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…
A new kind of diagrams is presented, showing the causal structure of bimetric interactions.
This note is devotes to some remarks regarding the use of variational methods, of minimax type, to establish continuity type results
In this note, we give an exposition of the construction of Seiberg-Witten invariants.
We give an elementary theory of Henselian local rings and construct the Henselization of a local ring. All our theorems have an algorithmic content.
We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts…
We propose to use orthologic as the basis for designing type systems supporting intersection, union, and negation types in the presence of subtyping assumptions. We show how to extend orthologic to support monotonic and antimonotonic…