Non-binary error correcting codes with noiseless feedback, localized errors, or both

摘要

A famous problem in Coding Theory consists in finding good bounds for the maximal size M(n, t, q) of a t-error correcting code over a q-ary alphabet Q = {0, 1,..., q - 1} with block length n. This code concept is suited for communication over a q-ary channel with input alphabet X = Q and output alphabet y = Q, where a word of length n sent by the encoder is changed by the channel in at most t letters. Here neither the encoder nor the decoder knows in advance where the errors, that is changes of letters, occur.