Minimal distance lexicographic codes over an infinite alphabet

The author investigates the properties of minimal distance lexicographic codes, or lexicode, over the ordered infinite alphabet N=(0,1,2...). The author presents a method for computing the basis of such a code. It is shown that any lexicographic code S with minimal distance d has a unique basis where each basis vector is a one followed by a string of zeros, followed by d-1 nonzero digits a/sub ij/. Furthermore, the matrix A=(a/sub ij/) has no singular minors over the nim-field. The dual code when S has finite length is also computed. The author develops a systematic approach to determine which words belong to these lexicodes.<
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