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This paper studies the problem of constructing codes correcting deletions in arrays. Under this model, it is assumed that an $n \times n$ array can experience deletions of rows and columns. These deletion errors are referred to as $({t_{\mathrm {r}}}, {t_{\mathrm {c}}})$ -criss-cross deletions if ${t_{\mathrm {r}}}$ rows and ${t_{\mathrm {c}}}$ columns are deleted, while a code correcting these deletion patterns is called a $({t_{\mathrm {r}}}, {t_{\mathrm {c}}})$ -criss-cross deletion correction code. The definitions for criss-cross insertions are similar. It is first shown that when $t_{r}=t_{c}$ the problems of correcting criss-cross deletions and criss-cross insertions are equivalent. The focus of this paper lies on the case of (1, 1)-criss-cross deletions. A non-asymptotic upper bound on the cardinality of (1, 1)-criss-cross deletion correction codes is shown which assures that the redundancy is at least $2n-3+2\log n$ bits. A code construction with an existential encoding and an explicit decoding algorithm is presented. The redundancy of the construction is at most $2n+4 \log n + 7 +2 \log e$. A construction with explicit encoder and decoder is presented. The explicit encoder adds an extra $5\log n + 5$ bits of redundancy to the construction. [ABSTRACT FROM AUTHOR]

Interleaved Reed–Solomon codes admit efficient decoding algorithms which correct burst errors far beyond half the minimum distance in the random errors regime, e.g., by computing a common solution to the Key Equation for each Reed–Solomon code, as described by Schmidt et al. If this decoder does not succeed, it may either fail to return a codeword or miscorrect to an incorrect codeword, and good upper bounds on the fraction of error matrices for which these events occur are known. The decoding algorithm immediately applies to interleaved alternant codes as well, i.e., the subfield subcodes of interleaved Reed–Solomon codes, but the fraction of decodable error matrices differs, since the error is now restricted to a subfield. In this paper, we present new general lower and upper bounds on the fraction of error matrices decodable by Schmidt et al.’s decoding algorithm, thereby making it the only decoding algorithm for interleaved alternant codes for which such bounds are known. [ABSTRACT FROM AUTHOR]