Shimura curves and codes
Jacobus H. Lint, Gerard van der Geer · Birkhäuser Basel eBooks · 1988
One of the problems of coding theory is to find codes over the field Fq for which the ratios $$ \frac{d}{n} $$ and $$ \frac{k}{n} $$ (with d the minimum distance, k the dimension and n the word length) are as large as possible. To a (linear) code we can associate a pair (δ,R) with δ = δ /n, R = k/n in the unit square [0,1]×[0,1]. We consider the set Vq of all such pairs (δ,R) obtained from linear codes and we let Uq be the set of limit points of Vq. Manin proved the following theorem about Uq, see [5,6].