7 papers
Linear exact repair schemes for free MDS and Reed-Solomon codes over Galois rings
Daniel P. Bossaller, Hiram H. López
Codes over rings, especially over Galois rings, have been extensively studied for nearly three decades due to their similarity to linear codes over finite fields. A distributed sto…
The trace dual of nonlinear skew cyclic codes
Daniel Bossaller, Daniel Herden, Indalecio Ruiz-Bolaños
Codes which have a finite field as their alphabet but which are only linear over a subfield are a topic of much recent interest due to their utili…
Nonlinear Skew Quasi-Cyclic Codes
Daniel Bossaller, Daniel Herden, Indalecio Ruiz-Bolanos
This article explores nonlinear analogues of skew quasi-cyclic codes of index~, i.e., -submodules of $\left(\mathbb{F}_{q^m}[X;σ]/(X^n - 1)\right)^\ell…
Forcing a Basis into -Free Groups
Daniel Bossaller, Daniel Herden, Alexandra V. Pasi
In this paper, we address the question of when a non-free -free group can be be free in a transitive cardinality-preserving model extension. Using the -invariant,…
Ideal Extensions and Directly Infinite Algebras
Daniel P. Bossaller
Directly infinite algebras, those algebras, which have a pair of elements and where , are well known to have a sub-algebra isomorphic to ,…
A Family of Almost Invertible Infinite Matrices
Daniel P. Bossaller
An algebraic analogue of the family of Fredholm operators is introduced for the family of row and column finite matrices, dubbed "Fredholm matrices." In addition, a measure is intr…
On the Associativity of Infinite Matrix Multiplication
Daniel P. Bossaller, Sergio R. López-Permouth
A natural definition of the product of infinite matrices mimics the usual formulation of multiplication of finite matrices with the caveat (in the absence of any sense of convergen…