On improved asymptotic bounds for codes from global function fields

Authors:
Siman Yang;Lulu Qi
Affiliations:
Department of Mathematics, East China Normal University, Shanghai, China 200241;Department of Mathematics, East China Normal University, Shanghai, China 200241
Venue:
Designs, Codes and Cryptography
Year:
2009

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Abstract

For an arbitrary prime power q, let αq be the standard function in the asymptotic theory of codes, that is, αq(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 αq(δ). In recent years several authors established various lower bounds on αq(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 + logq (1 + 2/q3) + logq (1 + (q - 1)/q6) can be achieved for certain values of q and certain ranges of δ.