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This paper gives new methods of constructing {\it symmetric self-dual codes}over a finite field $GF(q)$ where $q$ is a power of an odd prime. These methodsare motivated by the well-known Pless symmetry codes and quadratic doublecirculant codes. Using these methods, we construct an amount of symmetricself-dual codes over $GF(11)$, $GF(19)$, and $GF(23)$ of every length less than42. We also find 153 {\it new} self-dual codes up to equivalence: they are$[32, 16, 12]$, $[36, 18, 13]$, and $[40, 20,14]$ codes over $GF(11)$, $[36,18, 14]$ and $[40, 20, 15]$ codes over $GF(19)$, and $[32, 16, 12]$, $[36, 18,14]$, and $[40, 20, 15]$ codes over $GF(23)$. They all have new parameters withrespect to self-dual codes. Consequently, we improve bounds on the highestminimum distance of self-dual codes, which have not been significantly updatedfor almost two decades.

An improved upper bound on self-dual codes over finite fields $GF(11), GF(19)$, and $GF(23)$