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This paper gives some theory and efficient design of binary block codes capable of controlling the deletions of the symbol “0” (referred to as 0-deletions) and/or the insertions of the symbol “0” (referred to as 0-insertions). This problem of controlling 0-deletions and/or 0-insertions (referred to as 0-errors) is shown to be equivalent to the efficient design of L1 metric asymmetric error control codes over the natural alphabet, IIN . In this way, it is shown that the t0 -insertion correcting codes are actually capable of controlling much more; namely, they can correct t0 -errors, detect (t+1)0 -errors and, simultaneously, detect all occurrences of only 0-deletions or only 0-insertions in every received word (briefly, they are t -Symmetric 0-Error Correcting/ (t+1) -Symmetric 0-Error Detecting/All Unidirectional 0-Error Detecting ( t -Sy0EC/ (t+1) -Sy0ED/AU0ED) codes). From the relations with the L1 distance error control codes, new improved bounds are given for the optimal t0 -error correcting codes. Optimal non-systematic code designs are given. Decoding can be efficiently performed by algebraic means using the Extended Euclidean Algorithm (EEA). 

In this paper the theory and design of codes capable of correcting t insertion/deletion of the symbol 0 in each and every bucket of zeros (i. e., zeros in between two consecutive ones) are studied. It is shown that this problem is related to the zero error capacity achieving codes in limited magnitude error channel. Close to optimal non-systematic code designs and the encoding/decoding algorithms are described.