Formalizing building-up constructions of self-dual codes through isotropic lines in Lean

Excerpt

arXiv:2604.08485v2 Announce Type: replace-cross Abstract: The purpose of this paper is two-fold. First, we show that, after a specified form isometry, the two-coordinate reduction in the binary Hilbert-symbol realization of Chinburg and Zhang is inverse to Kim's building-up construction, up to permutation equivalence. Second, for $q\equiv1\pmod4$, we develop a $q$-ary analogue of this reduction-and-extension mechanism. The identity $c^2=-1$ yields the isotropic line governing the split construct