Chuang-Qiang Hu

MDS Algebraic Geometry Codes of Square-Root Length on Hyperelliptic Curves

For every fixed genus $g\geq2$ and every $0<\rho<1$, we construct maximum distance separable (MDS) algebraic geometry codes over $\F_q$ for all sufficiently large odd squares $q$. Their parameters are $\bigl[n,\lfloor\rho n\rfloor,n-\lfloor\rho n\rfloor+1\bigr]_q$ with $n=\sqrt q+1+O_g(q^{1/4})$. The codes use full Rie...