On L1-distance error control codes

This paper gives some theory and design of efficient codes capable of controlling (i. e., correcting/detecting/correcting erasure) errors measured under the L₁ 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_m s information digits.