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Block Decomposition of Generalized Quaternion Group Codes

In the semisimple group algebra Fq[Q4n] (field characteristic coprime to 4n), determining the components of a code's Wedderburn decomposition from its generating idempotent, expressed through the irreducible and reciprocal factors of x^n-1 and x^n+1, and applying this to describe the blocks of codes induced by cyclic group codes.

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Block components of generalized quaternion group codes Nadja Willenborg1

Studies linear codes realized as subspaces of the generalized quaternion group algebra Fq[Q4n], in the semisimple case where the field characteristic is coprime to 4n. In that regime every code has a…