arXiv subjects
Publications and source records attributed to Carlos Galindo.
We use affine variety codes and their subfield-subcodes for obtaining quantum stabilizer codes via the CSS code construction. With this procedure, we get codes with good parameters and a code whose parameters exceed the CSS quantum Gilbert-Varshamov bound given by Feng and Ma.
We solve the Poincaré problem for plane foliations with only one dicritical divisor. Moreover, in this case, we give an algorithm that decides whether a foliation has a rational first integral and computes it in the affirmative case. We also provide an algorithm to compute a rational first integral of prefixed genus $g\neq 1$ of any type of plane foliation $\cf$. When the number of dicritical divisors dic$(\cf)$ is larger than two, this algorithm depends on suitable families of invariant curves. When dic$(\cf) = 2$, it proves that the degree of the rational first integral can be bounded only in terms of $g$, the degree of $\cf$ and the local analytic type of the dicritical singularities of $\cf$.
We introduce the class of plane valuations at infinity and prove an analogue to the Abhyankar-Moh (semigroup) Theorem for it.
For a simple complete ideal $\wp$ of a local ring at a closed point on a smooth complex algebraic surface, we introduce an algebraic object, named Poincaré series $P_{\wp}$, that gathers in an unified way the jumping numbers and the dimensions of the vector space quotients given by consecutive multiplier ideals attached to $\wp$. This paper is devoted to prove that $P_{\wp}$ is a rational function giving an explicit expression for it.