Designs and full-rank STBCs from DFT domain description of cyclic codes

Viewing an n length vector over F
_q

^m
as an mtimesn matrix over F
_q
, by expanding each entry of the vector with respect to a basis of F
_q

^m
over F
_q
, the rank weight of the n length vector over F
_q

^m
is the rank of the corresponding mtimesn matrix over F
_q
. It is known that under some conditions, n-length cyclic codes over F
_q

^m
, (n|q
^m
-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 F
_q
where 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 F
_q

^m
, for r transmit antennas, where rlesn and r|m