For an arbitrary prime power q, let α q be the standard function in the asymptotic theory of codes, that is, α q (δ) is the largest asymptotic information rate that can be achieved by a sequence of q-ary codes with a given asymptotic relative minimum distance δ. A central problem in the asymptotic theory of codes is to find lower bounds on α q (δ). In recent years several authors established various lower bounds on α q (δ). In this paper, we present a further improved lower bound by extending a result of Niederreiter and Özbudak (Finite Fields Appl 13: 423–443, 2007). In particular, we show that the bound 1 − δ − A(q)−1 + log q (1 + 2/q 3) + log q (1 + (q − 1)/q 6) can be achieved for certain values of q and certain ranges of δ.
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