A generalized Gilbert-Varshamov bound derived via analysis of a code-search algorithm

A generalization of the Gilbert-Varshamov bound that is applicable to block codes whose codewords must be drawn from irregular sets is derived. The bound improves by a factor of four a similar result derived by V.D. Kolesnik and V.Y. Krachkovsky (1991). This generalization is derived by analysing a code search algorithm referred to as the altruistic algorithm. This algorithm iteratively deletes potential codewords so that at each iteration the candidate is removed. The bound is derived by demonstrating that, as the algorithm proceeds, the average volume of a sphere of a given radius approaches the maximum such volume and so a bound previously expressed in terms of the maximum volume can in fact be expressed in terms of the average volume. Examples of applications where the bound is relevant include error-correcting (d,k) codes and binary codes for code division multiple access.<
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