Multiple Criss-Cross Insertion and Deletion Correcting Codes

This paper investigates the problem of correcting multiple criss-cross insertions and deletions in arrays. More precisely, we study unique recovery $n \times n$ arrays affected by notation="LaTeX">${t}$ -criss-cross deletions defined as any combination notation="LaTeX">${t_{\mathrm {r}}}$ row {c}}}$ column such that {r}}}+ {t_{\mathrm {c}}}= {t}$ for a given notation="LaTeX">$t$ . We show an equivalence between -criss-cross code insertions/deletions has redundancy at least notation="LaTeX">${t} n + {t}\log - \log ({t}!)$ Then, present existential construction insertion/deletion with bounded from above \mathcal {O}({t}^{2} ^{2} n)$ The main ingredients presented are systematic binary -deletion codes Gabidulin codes. first ingredient helps locating indices inserted/deleted rows columns, thus transforming insertion/deletion-correction into row/column erasure-correction which is then solved using second ingredient.