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This paper investigates the problem of correcting multiple criss-cross insertions and deletions in arrays. More precisely, we study the unique recovery of $n times n$ arrays affected by $t$-criss-cross deletions defined as any combination of $t_r$ row and $t_c$ column deletions such that $t_r + t_c = t$ for a given $t$. We show an equivalence between correcting $t$-criss-cross deletions and $t$-criss-cross insertions and show that a code correcting $t$-criss-cross insertions/deletions has redundancy at least $tn + t log n - log(t!)$. Then, we present an existential construction of $t$-criss-cross insertion/deletion correcting code with redundancy bounded from above by $tn + mathcal{O}(t^2 log^2 n)$. The main ingredients of the presented code construction are systematic binary $t$-deletion correcting codes and Gabidulin codes. The first ingredient helps locating the indices of the inserted/deleted rows and columns, thus transforming the insertion/deletion-correction problem into a row/column erasure-correction problem which is then solved using the second ingredient.
In this paper motivated from subspace coding we introduce subspace-metric and subset-metric codes. These are coordinate-position independent pseudometrics and suitable for the folded codes introduced by Guruswami and Rudra. The half-Singleton upper b
Motivated by applications in machine learning and archival data storage, we introduce function-correcting codes, a new class of codes designed to protect a function evaluation of the data against errors. We show that function-correcting codes are equ
The concept of asymmetric entanglement-assisted quantum error-correcting code (asymmetric EAQECC) is introduced in this article. Codes of this type take advantage of the asymmetry in quantum errors since phase-shift errors are more probable than qudi
We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting schemes can
Recent advances in DNA sequencing technology and DNA storage systems have rekindled the interest in deletion channels. Multiple recent works have looked at variants of sequence reconstruction over a single and over multiple deletion channels, a notor