Related papers: Recent advances on minimal codes
In this paper, we construct new families of convolutional codes. Such codes are obtained by means of algebraic geometry codes. Additionally, more families of convolutional codes are constructed by means of puncturing, extending, expanding…
We discuss applications of minimal surfaces to comparison geometry.
This paper considers the equivalence problem for quasi-cyclic codes over finite fields. The results obtained are used to construct isodual quasi-cyclic codes.
Traditionally, computer programming has been the prerogative of professional developers using textual programming languages such as C, Java, or Python. Low-code programming promises an alternative: letting citizen developers create programs…
Two broad classes of graphical modeling problems for codes can be identified in the literature: constructive and extractive problems. The former class of problems concern the construction of a graphical model in order to define a new code.…
We introduce the notion of watching systems in graphs, which is a generalization of that of identifying codes. We give some basic properties of watching systems, an upper bound on the minimum size of a watching system, and results on the…
We introduce the first geometric construction of codes in the sum-rank metric, which we called linearized Algebraic Geometry codes, using quotients of the ring of Ore polynomials with coefficients in the function field of an algebraic…
The Gale transform, an involution on sets of points in projective space, appears in a multitude of guises, in subjects as diverse as optimization, coding theory, theta-functions, and recently in our proof that certain general sets of points…
A minimal code is a linear code where the only instance that a codeword has its support contained in the support of another codeword is when the codewords are scalar multiples of each other. Ashikhmin and Barg gave a sufficient condition…
Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This…
We introduce new yet easily accessible codes for elements of $GL_r(A)$ with $A$ the adelic ring of a (dimension one) function field over a finite field. They are linear codes, and coincide with classical algebraic geometry codes when $r=1$.…
In the past few years, the study of receptive field codes has been of large interest to mathematicians. Here we give a complete characterization of receptive field codes realizable by connected receptive fields and we give the minimal…
Minimal linear codes have interesting applications in secret sharing schemes and secure two-party computation. This paper uses characteristic functions of some subsets of $\mathbb{F}_q$ to construct minimal linear codes. By properties of…
We present an introduction to the theory of algebraic geometry codes. Starting from evaluation codes and codes from order and weight functions, special attention is given to one-point codes and, in particular, to the family of Castle codes.
A new construction of codes from old ones is considered, it is an extension of the matrix-product construction. Several linear codes that improve the parameters of the known ones are presented.
A construction is presented that allows to produce subspace codes of long length using subspace codes of shorter length in combination with a rank metric code. The subspace distance of the resulting code, called linkage code, is as good as…
In these notes we aim at bringing together design theory and projective geometry over a ring. Both disciplines are well established, but the results on the interaction between them seem to be rare and scattered over the literature. Thus our…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…
An index $e$ in a numbering of partial-recursive functions is called minimal if every lesser index computes a different function from $e$. Since the 1960's it has been known that, in any reasonable programming language, no effective…
In this paper we study the algebraic-geometry of any one-point code on the Hermitian curve. Moreover, we characterize the minimum-weight codewords of some of their dual codes and describe many their small-weight codewords.