Properties of dual codes defined by nondegenerate forms. (English) Zbl 1423.94156
Summary: 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.
Keywords:
Frobenius ring; sesquilinear form; bilinear form; dual code; generating character; MacWilliams identitiesReferences:
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