Construction of optimal few-weight binary and quaternary linear codes using multivariable functions

In this talk, we discuss how to find infinite families of few weight (near-) optimal binary and quaternary linear codes. Our construction methods mainly employ the shortening method and certain multivariable functions. Using our construction methods, new infinite families of (near-) optimal few-weight binary and quaternary linear codes are obtained. As an application of our binary linear codes, we produce support t-designs (t = 2 or 3) which cannot be determined by the Assmus-Mattson Theorem. Additionally, we derive many (near-) optimal quantum codes from the dual codes of our binary code families using the CSS construction.