New upper bounds for grain-correcting and grain-detecting codes

Abstract

New upper bounds on the size and the rate of grain-correcting codes are presented. The new upper bound on the size of t-grain-correcting codes of length n improves on the best known upper bounds for certain values of n and t, whereas the new upper bound on the asymptotic rate of [τn]-grain-correcting codes of length n improves on the previously known upper bounds on the interval τ ∈ (0, ⅛]. A lower bound of 1/2 log2 n on the minimum redundancy of ∞-grain-detecting codes of length n is presented.