Properties of dual codes defined by nondegenerate forms

Abstract

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 identities

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