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Abstract An (n, R) -covering sequence is a cyclic sequence whose consecutive n -tuples form a code of length n and covering radius R. Using several construction methods improvements of the upper bounds on the length of such sequences for n 20 n ≤ 20 and 1 R 3 1 ≤ R ≤ 3, are obtained. The definition is generalized in two directions. An (n, m, R) -covering sequence code is a set of cyclic sequences of length m whose consecutive n -tuples form a code of length n and covering radius R. The definition is also generalized to arrays in which the m n m × n sub-matrices form a covering code with covering radius R. We prove that asymptotically there are covering sequences that attain the sphere-covering bound up to a constant factor.
Chee et al. (Thu,) studied this question.