# Designs and Full-Rank STBCs from DFT Domain Description of Cyclic Codes

Sripati, U and Shashidhar, V and Rajan, Sundar B (2004) Designs and Full-Rank STBCs from DFT Domain Description of Cyclic Codes. In: International Symposium on Information Theory, 2004. ISIT 2004, 27 June-2 July, Chicago, 338 -338.

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Viewing an $n$ length vector over $F_{q^m}$ as an ${m}\times{n}$ 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 ${m}\times{n}$ matrix over $F_q$. It is known that under some conditions, $n$-length cyclic codes over $F_{q^m}$, $({n}\backslash{q}^m-1\hspace{5 mm}and\hspace{5 mm}{m}\leq{n})$ 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 ${r}\leq{n}$ and $r|m$.