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The equivalence of space-time codes and codes defined over finite fields and Galois rings

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  • Space-time codes for a wide variety of channels have the property that the diversity of a pair of codeword matrices is measured by the vanishing or non-vanishing of polynomials in the entries of the matrices. We show that for every such channel: I) There is an appropriately-defined notion of approximation of space-time codes such that each code is arbitrarily well approximated by one whose alphabet lies in the field of algebraic numbers; II) Each space-time code whose alphabet lies in the field of algebraic numbers is an appropriately-defined lift from a corresponding space-time code defined over a finite field or a ''scaled'' lift from a Galois ring of arbitrary characteristic. This implies that all space-time codes can be designed over finite fields or over Galois rings of arbitrary characteristic and then lifted to complex matrices with entries in a number field.
    Mathematics Subject Classification: 94B60, 11T71, 14G50.


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