Singleton-type bounds for blot-correcting codes

Consider the transmission of codewords over a channel which introduces dependent errors. Thinking of two-dimensional codewords, such errors can be viewed as blots of a particular shape on the codeword. For such blots of errors the combinatorial metric was introduced by Gabidulin (1971) and it was shown that a code with distance d in combinatorial metric can correct d/2 blots. We propose an universal Singleton-type upper bound on the rate R of a blot-correcting code with the distance d in arbitrary combinatorial metric. The rate is bounded by R⩽1-(d-1)/D, where D is the maximum possible distance between two words in this metric