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May  2008, 2(2): 131-145. doi: 10.3934/amc.2008.2.131

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

David Grant 1, and  Mahesh K. Varanasi 2,

1. 

Department of Mathematics, University of Colorado at Boulder, Boulder, CO 80309-0395
2. 

Department of Electrical and Computer Engineering, University of Colorado at Boulder, Boulder, CO 80309-0425, United States

Received  October 2007 Revised  April 2008 Published  April 2008

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.
Keywords: Space-time codes, Galois rings., finite fields.
Mathematics Subject Classification: 94B60, 11T71, 14G5.
Citation: David Grant, Mahesh K. Varanasi. The equivalence of space-time codes and codes defined over finite fields and Galois rings. Advances in Mathematics of Communications, 2008, 2 (2) : 131-145. doi: 10.3934/amc.2008.2.131
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