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The State Of Lexicodes And Ferrers Diagram Rank-Metric Codes, Jared E. Antrobus

Theses and Dissertations--Mathematics

In coding theory we wish to find as many codewords as possible, while simultaneously maintaining high distance between codewords to ease the detection and correction of errors. For linear codes, this translates to finding high-dimensional subspaces of a given metric space, where the induced distance between vectors stays above a specified minimum. In this work I describe the recent advances of this problem in the contexts of lexicodes and Ferrers diagram rank-metric codes.

In the first chapter, we study lexicodes. For a ring R, we describe a lexicographic ordering of the left R-module Rⁿ. With this …