Properties of dual codes defined by nondegenerate forms

  • Steve Szabo
  • Jay A. Wood
Keywords: Frobenius ring, Sesquilinear form, Bilinear form, Dual code, Generating character, MacWilliams identities


Dual codes are defined with respect to non-degenerate sesquilinear or bilinear forms over a finite Frobenius ring. These dual codes have the properties one expects from a dual code: they satisfy a double-dual property, they have cardinality complementary to that of the primal code, and they satisfy the MacWilliams identities for the Hamming weight.


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