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, 1 ]. A lower bound of 1 log n on the minimum redundancy of ∞-grain-detecting codes 22 of length n is presented.