Johnson Bound Research Articles

Constructions of Nonbinary Codes Meeting the Johnson Bound

Constructions of Nonbinary Codes Meeting the Johnson Bound

Weakly Resolvable Block Designs and Nonbinary Codes Meeting the Johnson Bound

Weakly Resolvable Block Designs and Nonbinary Codes Meeting the Johnson Bound

Analysis of an algorithm used for finding Unipolar Orthogonal Codes

An Auto-Correlation and Cross-Correlation property of an Orthogonal Code enables the transfer of data with less interference. With more Orthogonal Codes, an Optical Fiber Communication channel can support a large number of users efficiently and reliably with high bandwidth. This paper analyses an algorithm used for finding Unipolar Orthogonal Codes using four major parameters (n, w, λa, and λc) where n is the length of a binary string, w is the weight of the string n (number of one’s in the string), λa is the Auto-Correlation, and λc is the Cross-Correlation. These four parameters jointly with the Johnson Bound (JA) condition are used in the algorithm. The paper illustrates the analysis of a possible number of Orthogonal Code Sets calculated using Orthogonal Codes generated from a software code that is based on the algorithm in consideration. The data analysis is carried out and the findings are summarized.

Some sequences of optimal constant weight codes

We introduce some sequences of binary constant weight codes which are constructed from the affine constructions of balanced incomplete block designs. They give the values for the function [Formula: see text] of constant weight codes, and they are optimal since those values reach the Johnson Bound. We focus on the values obtained by this method.

Distributed scheduling for disconnected cooperation

The dissertation studies how distributed devices that are disconnected for long and unknown periods can efficiently perform a set of tasks. Given n distributed devices that must perform t independent tasks, known to each device, the goal is to schedule work of the devices locally, in the absence of communication, so that when communication is established between some devices at some later point of time, the devices that connect have performed few tasks redundantly beyond necessity. The dissertation gives a lower bound on redundant work, and randomized and deterministic schedules, that allow devices to avoid doing redundant work provably well. The lower bound shows how the wasted work increases as the devices progress in their work. When each disconnected device randomly selects its next task, from among the tasks remaining to be done, then the amount of work duplicated by any devices that reconnect, is close to the lower bound in a precise sense. In order to derandomize the construction of schedules, techniques from design theory, linear algebra, and graph theory are used. The topics developed within the dissertation are related to the theory of latin squares and coding theory. For example the lower bound shown in the dissertation generalizes the Second Johnson Bound. The dissertation also studies scheduling problems for shared memory systems. It shows a method for creating near-optimal instances of an algorithm of Anderson and Woll. The dissertation also shows a work-optimal deterministic algorithm for the asynchronous Certified Write-All problem.