Bull. Korean Math. Soc. 2015; 52(3): 915-923
Printed May 31, 2015
https://doi.org/10.4134/BKMS.2015.52.3.915
Copyright © The Korean Mathematical Society.
Jon-Lark Kim and Yoonjin Lee
Sogang University, Ewha Womans University
Self-dual codes have been actively studied because of their connections with other mathematical areas including $t$-designs, invariant theory, group theory, lattices, and modular forms. We presented the building-up construction for self-dual codes over $GF(q)$ with $q \equiv 1 \pmod 4$, and over other certain rings (see~\cite{KimLee},~\cite{KimLee2}). Since then, the existence of the building-up construction for the open case over $GF(q)$ with $q=p^r \equiv 3 \pmod 4$ with an odd prime $p$ satisfying $p \equiv 3 \pmod 4$ with $r$ odd has not been solved. In this paper, we answer it positively by presenting the building-up construction explicitly. As examples, we present new optimal self-dual $[16,8,7]$ codes over $GF(7)$ and new self-dual codes over $GF(7)$ with the best known parameters $[24,12,9]$.
Keywords: building-up construction, linear codes, self-dual codes
MSC numbers: Primary 94B05
2018; 55(5): 1371-1387
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