New Qutrit Codes from Pure and Bordered Multidimensional Circulant Construction

Abstract

We use multidimensional circulant approach to construct new qutrit stabilizer $\dsb{\ell, 0, d}$ codes with parameters $(\ell ,d)\in \{(51,16),(52,16),(54,17),(55,17),(57,17)\}$ through symplectic self-dual additive codes over $\F_9$. In addition to these five new codes, we use bordered construction to derive two more qutrit codes with parameters $(\ell ,d)\in \{(53,16),(56,17)\}$ that improve upon previously best known parameters.