Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ADDITIVE SELF-DUAL CODES OVER FIELDS OF EVEN ORDER

  • Dougherty, Steven T. (Department of Mathematics University of Scranton) ;
  • Kim, Jon-Lark (Department of Mathematics Sogang University) ;
  • Lee, Nari (Department of Mathematics Sogang University)
  • Received : 2016.10.19
  • Accepted : 2017.11.22
  • Published : 2018.03.31
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Abstract

We examine various dualities over the fields of even orders, giving new dualities for additive codes. We relate the MacWilliams relations and the duals of ${\mathbb{F}}_{2^{2s}}$ codes for these various dualities. We study self-dual codes with respect to these dualities and prove that any subgroup of order $2^s$ of the additive group is a self-dual code with respect to some duality.

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References

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