INTEGER t-SHIFT CODES AND FACTORING ABELIAN GROUPS

Year 2011, Volume: 10 Issue: 10, 25 - 36, 01.12.2011

Sándor Szabó

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.

Keywords

integer codes, shift codes, single-error correcting perfect codes, splitting and factoring abelian groups

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