Locating–dominating codes in paths

Burst Error Correcting Codes and Lattice Paths

Perfect Codes in Cartesian Products of 2-Paths and Infinite Paths

We introduce and study a common generalization of 1-error binary perfect codes and perfect single error correcting codes in Lee metric, namely perfect codes on products of paths of length 2 and of infinite length. Both existence and nonexistence results are given.

Identifying codes and locating-dominating sets on paths and cycles

Let G = (V,E) be a graph and let r ≥ 1 be an integer. For a set D ⊆ V , define Nr[x] = {y ∈ V : d(x, y) ≤ r} and Dr(x) = Nr[x] ∩ D, where d(x, y) denotes the number of edges in any shortest path between x and y. D is known as an r-identifying code (r-locating-dominating set, respectively), if for all vertices x ∈ V (x ∈ V \D, respectively), Dr(x) are all nonempty and different. In this paper, w...

Single-Point Visibility Constraint Minimum Link Paths in Simple Polygons

We address the following problem: Given a simple polygon $P$ with $n$ vertices and two points $s$ and $t$ inside it, find a minimum link path between them such that a given target point $q$ is visible from at least one point on the path. The method is based on partitioning a portion of $P$ into a number of faces of equal link distance from a source point. This partitioning is essentially a shor...

One-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes

We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...