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arXiv · 2203.11341

Binary codes that do not preserve primitivity

Štěpán Holub·Martin Raška·Štěpán Starosta
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Abstract

A code $X$ is not primitivity preserving if there is a primitive list ${\mathbf w} \in {\tt lists} X$ whose concatenation is imprimitive. We formalize a full characterization of such codes in the binary case in the proof assistant Isabelle/HOL. Part of the formalization, interesting on its own, is a description of $\{x,y\}$-interpretations of the square $xx$ if $|y| \leq |x|$. We also provide a formalized parametric solution of the related equation $x^jy^k = z^\ell$.

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Štěpán Holub, Martin Raška, Štěpán Starosta. 2022-03-21. Binary codes that do not preserve primitivity. https://doi.org/10.1007/s10817-023-09674-2

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