Normalized minimum determinant calculation for multi-block and asymmetric space-time codes

Authors:
Camilla Hollanti;Hsiao-feng Lu
Affiliations:
Department of Mathematics, University of Turku, Finland;Department of Communication Engineering, National Chung-Cheng University, Chia-yi, Taiwan
Venue:
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Year:
2007

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Abstract

The aim of this paper is to show the connection between certain, previously constructed multi-block and asymmetric space-time codes. The Gram determinants of the two constructions coincide, and hence the corresponding lattices share the same density. Using the notion of density, we define the normalized minimum determinant and give an implicit lower bound depending on the center of the cyclic division algebra in use. The calculation of the normalized minimum determinant is then performed in practice by using explicit code constructions.