Quasi-perfect Lee distance codes

A construction of perfect/quasiperfect Lee distance codes in Z/sub K//sup 2/ is introduced. For this class of codes, a constant time encoding scheme is defined, the minimum code distance is derived, and the maximum covering radius is calculated. Efficient decoding schemes are investigated and developed. In general, a code of this class can be decoded in O(t/sub 1/), where t/sub 1/ is the number of errors that can be corrected. Special cases, however, can be decoded in constant time.

[1]  Karel A. Post.  Nonexistence Theorems on Perfect Lee Codes over Large Alphabets , 1975, Inf. Control..

[2]  Jong-Hyun Kim,et al.  I/O placement strategies and their data locality sensitivities in k/spl times/k toroidal networks , 1997, Proceedings High Performance Computing on the Information Superhighway. HPC Asia '97.

[3]  Jaakko Astola.  On the asymptotic behaviour of Lee-codes , 1984, Discret. Appl. Math..

[4]  Yaagoub Ashir,et al.  Lee Distance and Topological Properties of k-ary n-cubes , 1995, IEEE Trans. Computers.

[5]  Jaakko Astola.  Concatenated codes for the Lee metric , 1982, IEEE Trans. Inf. Theory.

[6]  J. Astola.  THE LEE-SCHEME AND BOUNDS FOR LEE-CODES , 1982 .

[7]  Quentin F. Stout,et al.  PERFECT DOMINATING SETS , 1990 .

[8]  Myung M. Bae,et al.  Resource placement in torus-based networks , 1996, Proceedings of International Conference on Parallel Processing.

[9]  Elwyn R. Berlekamp,et al.  Algebraic coding theory , 1984, McGraw-Hill series in systems science.

[10]  Jaakko Astola.  An Elias-type bound for Lee codes over large alphabets and its application to perfect codes , 1982, IEEE Trans. Inf. Theory.

[11]  Paul H. Siegel,et al.  Lee-metric BCH codes and their application to constrained and partial-response channels , 1994, IEEE Trans. Inf. Theory.

[12]  Jack K. Wolf,et al.  On Channels and Codes for the Lee Metric , 1971, Inf. Control..

[13]  Bader Fahed Albedaiwi Almohammad.  On resource placements and fault-tolerant broadcasting in toroidal networks , 1998 .