This paper gives some theory and design of efficient codes capable of controlling (i. e., correcting/detecting/correcting erasure) errors measured under the L<inf>1</inf> distance defined over m-ary words, 2 ≤ m ≤ +∞. We give the combinatorial characterizations of such codes, some general code designs and the efficient decoding algorithms. Then, we give a class of linear and systematic m-ary codes, m = sp with s∈IN and p a prime, which are capable of controlling d ≤ p−1 errors. If n and k∈IN are respectively the length and dimension of a BCH code over GF(p) with minimum Hamming distance d + 1 then the new codes have length n and k′ = k + r log<inf>m</inf> s information digits.
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