Block components of generalized quaternion group codes
Type
book review
Date Issued
2025-01-02
Author(s)
Willenborg, Nadja
Abstract
Codes in the generalized quaternion group algebra F q [Q 4n ] are considered. Restricting to charF q ∤ 4n the structure of an arbitrary code C ⊆ F q [Q 4n ] is described via the Wedderburn decomposition. Moreover it is known that in this case every code C ⊆ F q [Q 4n ] has a generating idempotent λ ∈ F q [Q 4n ]. Given the generating idempotent of a code C we determine the different components in its decomposition C ∼ = r+s j=1 C j ⊕ k+t i=1 C ′ i. Afterwards we apply this result to describe the blocks of codes induced by cyclic group codes.
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