It has been known that a binary code with parameters [n, k, d] does exist provided that k Hamming balls with diameter d-2 may be fitted in n-dimensional binary field. This simple bound, known as the Varshamov bound, relies on the fact that the number of linear combinations of d vectors from a collection of n vectors cannot be larger than the number of combinations of d or less elements from an n-element set. In this paper, we present several results that extend this counting mechanism and improve the binary Varshamov bound.
Linear codes Greedy codes Lexicodes Gilbert-Varshamov bound Greedy algorithms
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