Title :
Minimal distance lexicographic codes over an infinite alphabet
Author :
Herscovici, David S.
Author_Institution :
Dept. of Math., MIT, Cambridge, MA, USA
fDate :
9/1/1991 12:00:00 AM
Abstract :
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 aij. Furthermore, the matrix A=(aij) 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
Keywords :
error correction codes; basis vector; dual code; infinite alphabet; lexicode; minimal distance lexicographic codes; Code standards; Game theory; Hamming distance; Linear code; Mathematics; Vectors; Writing;
Journal_Title :
Information Theory, IEEE Transactions on
