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Full-Text Articles in Algebra
Weight Distributions, Automorphisms, And Isometries Of Cyclic Orbit Codes, Hunter Lehmann
Weight Distributions, Automorphisms, And Isometries Of Cyclic Orbit Codes, Hunter Lehmann
Theses and Dissertations--Mathematics
Cyclic orbit codes are subspace codes generated by the action of the Singer subgroup Fqn* on an Fq-subspace U of Fqn. The weight distribution of a code is the vector whose ith entry is the number of codewords with distance i to a fixed reference space in the code. My dissertation investigates the structure of the weight distribution for cyclic orbit codes. We show that for full-length orbit codes with maximal possible distance the weight distribution depends only on q,n and the dimension of U. For full-length orbit codes with …
Analysis And Constructions Of Subspace Codes, Carolyn E. Troha
Analysis And Constructions Of Subspace Codes, Carolyn E. Troha
Theses and Dissertations--Mathematics
Random network coding is the most effcient way to send data across a network, but it is very susceptible to errors and erasures. In 2008, Kotter and Kschischang introduced subspace codes as an algebraic approach to error correcting in random network coding. Since this paper, there has been much work in constructing large subspace codes, as well as exploring the properties of such codes. This dissertation explores properties of one particular construction and introduces a new construction for subspace codes. We begin by exploring properties of irreducible cyclic orbit codes, which were introduced in 2011 by Rosenthal et al. As …