INTEGER t-SHIFT CODES AND FACTORING ABELIAN GROUPS

Abstract

Let p a be prime number. Using algebraic methods from the factorization theory of abelian groups we will prove a result about the structure of the 1-error correcting t-shift integer codes over the alphabet Zp in the special case when t is a prime. The algorithms to construct such codes can take advantage of this extra structural information in a straightforward manner and the search for these codes can be speed up dramatically.