Codes From the Suzuki Function Field
Gretchen L. Matthews · IEEE Transactions on Information Theory · 2004
We construct algebraic geometry (AG) codes from the function field F(2/sup 2n+1/)(x,y)/F(2/sup 2n+1/) defined by y(2/sup 2n+1/)-y=(x(2/sup 2n+/)-x) where n is a positive integer. These codes are supported by two places, and many have parameters that are better than those of any comparable code supported by one place of the same function field. To define such codes, we determine and exploit the structure of the Weierstrass gap set of an arbitrary pair of rational places of F(2/sup 2n+1/)(x,y)/F(2/sup 2n+1/). Moreover, we find some codes over F/sub 8/ with parameters that are better than any known code.