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arXiv · 2407.16256

Menichetti's nonassociative $G$-crossed product algebras and Menichetti codes

Susanne Pumpluen
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Abstract

We define the nonassociative Menichetti algebras which can be viewed as nonassociative crossed product algebras and then use them as ambient algebras for new linear error-correcting codes. More precisely, we take their left principal ideals to define linear codes which are in canonical one-to-one correspondence with these ideals, imitating the approach taken when defining right skew polycyclic codes as left principal ideals of Petit algebras. The approach is novel and will create large classes of new linear codes which are well behave because of their algebraic definition as ideals of an algebra. With the right choice of algebra the codes display symmetric and cyclic properties which promise efficient decoding algorithms.

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Susanne Pumpluen. 2026-09-14. Menichetti's nonassociative $G$-crossed product algebras and Menichetti codes. https://arxiv.org/abs/2407.16256

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