Low Density MDS Codes and Factors of Complete Graphs

Xu, L. and Bohossian, V. and Bruck, J. and Wagner, D. (1998) Low Density MDS Codes and Factors of Complete Graphs. Technical Report. California Institute of Technology. [CaltechPARADISE:1998.ETR025]

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Abstract

We reveal an equivalence relation between the construction of a new class of low density MDS array codes, that we call B-Code, and a combinatorial problem known as perfect one- factorization of complete graphs. We use known perfect one-factors of complete graphs to create constructions and decoding algorithms for both B-Code and its dual code. B-Code and its dual are optimal in the sense that (i) they are MDS, (ii) they have an optimal encoding property, i.e., the number of the parity bits that are affected by change of a single information bit is minimal and (iii) they have optimal length. The existence of perfect one-factorizations for every complete graph with an even number of nodes is a 35 years long conjecture in graph theory. The construction of B-codes of arbitrary odd length will provide an affirmative answer to the conjecture.

EPrint Type:	Monograph (Technical Report)
Additional Information:	[Alternate URL: http://www.paradise.caltech.edu/papers/etr025.ps]
Subjects:	All Records
ID Code:	24
Deposited By:	Jehoshua Bruck
Deposited On:	03 September 2002
Record Number:	CaltechPARADISE:1998.ETR025
Official Persistent URL:	http://resolver.caltech.edu/CaltechPARADISE:1998.ETR025
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