Bounds on Codes Derived by Counting Components in Varshamov Graphs |
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Authors: | Katie M. O’Brien Patrick Fitzpatrick |
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Affiliation: | (1) Department of Engineering Mathematics, University of Bristol, England, BS8 1TR;(2) Department of Mathematics, University College Cork, Ireland |
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Abstract: | We are interested in improving the Varshamov bound for finite values of length n and minimum distance d. We employ a counting lemma to this end which we find particularly useful in relation to Varshamov graphs. Since a Varshamov graph consists of components corresponding to low weight vectors in the cosets of a code it is a useful tool when trying to improve the estimates involved in the Varshamov bound. We consider how the graph can be iteratively constructed and using our observations are able to achieve a reduction in the over-counting which occurs. This tightens the lower bound for any choice of parameters n, k, d or q and is not dependent on information such as the weight distribution of a code. This work is taken from the author’s thesis [10] |
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Keywords: | Varshamov bound Varshamov graph Greedy codes |
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