Artyom Sharov – New upper bounds for grain-correcting and grain-detecting codes


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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 \ceil{\tau n}-grain-correcting codes of length n improves on the previously known upper bounds on the interval \tau\in (0,1/8]. A lower bound of 0.5\log_2(n) on the minimum redundancy of ?-grain-detecting codes of length n is presented.