Construction of binary linear codes via rational function fields (Q521865)

The authors present a novel construction of binary linear codes using the rational function field over characteristic two finite fields \(\mathbb{F}_q.\) Given \(r \leq (q^2 - q)/2 - 1,\) the method produces \([n,k,d]\) codes where \(n=q+1+2r,\) \(d \geq 2 \delta + 2,\) \(k \geq q + r - \delta \log_2 q\) for any \(\delta \geq 2.\) A number of examples are presented, many of which are optimal in the sense that the maximum distance is as large as possible.