Binary Array Codes Correcting a Single Criss-Cross Edit Error

The problem of constructing binary array codes capable of correcting criss-cross has attracted more attention due to such errors appearing in racetrack memories and DNA-based storage systems. In this paper, we investigated the constructions of binary array codes that can correct a single criss-cross edit error and the constructions of binary array codes that can correct a single (t,s)-burst criss-cross edit error, respectively. Specifically speaking, we first present a family of binary array codes that can correct a single criss-cross edit whose redundancy is 2nlogn+2n by using the Levenshtein codes capable of correcting a single edit error. Then, based on the above codes and array representation, we construct a class of binary array codes that can correct a single (t,s)-burst criss-cross edit error. The redundancy of such binary array codes is 2n(t+s)logn+2n(t+s). The decoding methods are incorporated in the proof of the corresponding theorem and the complexities of the decoding methods of both binary array codes are all O(n2). Moreover, the proposed binary array codes and decoding methods are validated through illustrative examples.