SPT(q, k, n)-Codes

Database motivations lead to the concept of SPT(q, k, n)-codes. These are q-ary codes of length n, minimum distance n−k+1 and have the property that for any possible k−1 coordinate positions there are two codewords that agree exactly there. We derive upper and lower bounds on the length of the code as function of q and k. The upper bounds use geometric arguments and bounds on spherical codes, the lower bounds are probabilistic.