Designs and full-rank STBCs from DFT domain description of cyclic codes
Udupi Sripati, V. Shashidhar, Balaji Sundar Rajan · 2004
Viewing an n length vector over Fqmas an mtimesn matrix over Fq, by expanding each entry of the vector with respect to a basis of Fqmover Fq, the rank weight of the n length vector over Fqmis the rank of the corresponding mtimesn matrix over Fq. It is known that under some conditions, n-length cyclic codes over Fqm, (n|qm-1 and mlesn) have full rank. In this paper, using this result we obtain a design using which we construct full-rank space-time block codes (STBCs) for m transmit antennas over signal sets matched to Fqwhere q=2 or q is a prime of the form 4k+1. We also propose a construction of STBCs using n-length cyclic codes over Fqm, for r transmit antennas, where rlesn and r|m