Strengthening the Gilbert–Varshamov bound

AbstractThe paper discusses some ways to strengthen (nonasymptotically) the Gilbert–Varshamov bound for linear codes. The unifying idea is to study a certain graph constructed on vectors of low weight in the cosets of the code, which we call the Varshamov graph. Various simple estimates of the number of its connected components account for better lower bounds on the minimum distance of codes, some of them known in the literature