New Nonbinary Self-Dual Codes

In this correspondence, we construct new self-dual codes over ₄, ₅, ₇ with larger minimum weights than the previously known self-dual codes, using construction methods based on circulant and negacirculant matrices. In particular, a self-dual $[36,18,13]$ code over ₇ is constructed which has a larger minimum weight than the previously known $[36,18]$ codes.