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AN EFFICIENT CONSTRUCTION OF SELF-DUAL CODES

  • Kim, Jon-Lark (Department of Mathematics Sogang University) ;
  • Lee, Yoonjin (Department of Mathematics Ewha Womans University)
  • Received : 2014.04.23
  • Published : 2015.05.31
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Abstract

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 $q{\equiv}1$ (mod 4), and over other certain rings (see [19], [20]). Since then, the existence of the building-up construction for the open case over GF(q) with $q=p^r{\equiv}3$ (mod 4) with an odd prime p satisfying $p{\equiv}3$ (mod 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].

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References

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