Binary Codes that Do Not Preserve Primitivity

Abstract

AbstractA code X is not primitivity preserving if there is a primitive list $$\mathbf {w}\in \texttt {lists}\, X$$ w ∈ 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 $$\{x,y\}$$ { x , y } -interpretations of the square xx if $$\left| y \right| \le \left| x \right| $$ y ≤ x . We also provide a formalized parametric solution of the related equation $$x^jy^k = z^\ell $$ x j y k = z ℓ .