All Outputs (27)

Finite nonassociative algebras obtained from skew polynomials and possible applications to (f, σ, δ)-codes (2017)
Journal Article
Pumpluen, S. (2017). Finite nonassociative algebras obtained from skew polynomials and possible applications to (f, σ, δ)-codes. Advances in Mathematics of Communications, 11(3), 615-634. https://doi.org/10.3934/amc.2017046

Let S be a unital ring, S[t; σ, δ] a skew polynomial ring where σ is an injective endomorphism and δ a left σ -derivation, and suppose f ε S[t; σ, δ] has degree m and an invertible leading coefficient. Using right division by f to define the multipl... Read More about Finite nonassociative algebras obtained from skew polynomials and possible applications to (f, σ, δ)-codes.

The automorphisms of Petit's algebras (2017)
Journal Article
Brown, C., & Pumpluen, S. (in press). The automorphisms of Petit's algebras. Communications in Algebra, https://doi.org/10.1080/00927872.2017.1327598

Let σ be an automorphism of a field K with fixed field F. We study the automorphisms of nonassociative unital algebras which are canonical generalizations of the associative quotient algebras K[t; σ]=fK[t; σ] obtained when the twisted polynomialf 2 K... Read More about The automorphisms of Petit's algebras.

Nonassociative differential extensions of characteristic p (2017)
Journal Article
Pumpluen, S. (2017). Nonassociative differential extensions of characteristic p. Results in Mathematics, 72(1-2), https://doi.org/10.1007/s00025-017-0656-x

Let F be a field of characteristic p. We define and investigate nonassociative differential extensions of F and of a finite-dimensional central division algebra over F and give a criterium for these algebras to be division. As special cases, we obtai... Read More about Nonassociative differential extensions of characteristic p.

Tensor products of nonassociative cyclic algebras (2015)
Journal Article
Pumpluen, S. (2016). Tensor products of nonassociative cyclic algebras. Journal of Algebra, 451, https://doi.org/10.1016/j.jalgebra.2015.12.007

We study the tensor product of an associative and a nonassociative cyclic algebra. The condition for the tensor product to be a division algebra equals the classical one for the tensor product of two associative cyclic algebras by Albert or Jacobson,... Read More about Tensor products of nonassociative cyclic algebras.

The nonassociative algebras used to build fast-decodable space-time block codes (2015)
Journal Article
Pumpluen, S., & Steele, A. (2015). The nonassociative algebras used to build fast-decodable space-time block codes. Advances in Mathematics of Communications, 9(4), https://doi.org/10.3934/amc.2015.9.449

Let K/F and K/L be two cyclic Galois field extensions and D a cyclic algebra. Given an invertible element d in D, we present three families of unital nonassociative algebras defined on the direct sum of n copies of D. Two of these families appear eit... Read More about The nonassociative algebras used to build fast-decodable space-time block codes.

Fast-decodable MIDO codes from non-associative algebras (2015)
Journal Article
Pumpluen, S., & Steele, A. (2015). Fast-decodable MIDO codes from non-associative algebras. International Journal of Information and Coding Theory, 3(1), https://doi.org/10.1504/IJICOT.2015.068695

By defining a multiplication on a direct sum of n copies of a given cyclic division algebra, we obtain new unital non-associative algebras. We employ their left multiplication to construct rate-n and rate-2 fully diverse fast ML-decodable space-time... Read More about Fast-decodable MIDO codes from non-associative algebras.

How to obtain division algebras used for fast-decodable space-time block codes (2014)
Journal Article
Pumpluen, S. (2014). How to obtain division algebras used for fast-decodable space-time block codes. Advances in Mathematics of Communications, 8(3), https://doi.org/10.3934/amc.2014.8.323

We present families of unital algebras obtained through a doubling process from a cyclic central simple algebra D, employing a K-automorphism tau and an invertible element d in D. These algebras appear in the construction of iterated space-time block... Read More about How to obtain division algebras used for fast-decodable space-time block codes.