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

Abstract

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 methods are motivated by the well-known Pless symmetry codes and quadratic double circulant codes. Using these methods, we construct an amount of symmetric self-dual codes over $GF(11)$, $GF(19)$, and $GF(23)$ of every length less than 42. 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 with respect to self-dual codes. Consequently, we improve bounds on the highest minimum distance of self-dual codes, which have not been significantly updated for almost two decades.

References in corpus (1)

• Self-dual codes over $GF(q)$ with symmetric generator matrices