Self-dual codes over commutative Frobenius rings

نویسندگان

  • Steven T. Dougherty
  • Jon-Lark Kim
  • Hamid Kulosman
  • Hongwei Liu
چکیده

We prove that self-dual codes exist over all finite commutative Frobenius rings, via their decomposition by the Chinese Remainder Theorem into local rings. We construct non-free self-dual codes under some conditions, using self-dual codes over finite fields, and we also construct free self-dual codes by lifting elements from the base finite field. We generalize the building-up construction for finite commutative Frobenius rings, showing that all self-dual codes with minimum weight greater than 2 can be obtained in this manner in cases where the construction applies.

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عنوان ژورنال:
  • Finite Fields and Their Applications

دوره 16  شماره 

صفحات  -

تاریخ انتشار 2010