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Line 14: : <math>H_q(x) = x\log_q(q-1)-x\log_qx-(1-x)\log_q(1-x).</math> The above result was proved by [[Edgar Gilbert]] for general code using the [[greedy method]] as [[Gilbert–Varshamov bound\|here]]. For [[linear code]], [[Rom Varshamov]] proved using the [[probabilistic method]] for the random linear code. This proof will be shown in the following part. '''''High-level proof:'''''

Gilbert–Varshamov bound for linear codes: Difference between revisions