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# Full Rank Distance Codes and Optimal STBC for BPSK Modulation

Manoj, KN and Rajan, Sundar B (2002) Full Rank Distance Codes and Optimal STBC for BPSK Modulation. In: IEEE International Symposium on Information Theory, 2002, June 30 - July 5,, Lausanne,Switzerland, p. 276.

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## Abstract

Viewing the codewords of an $[n,k]$ linear code over a field $F_{q^m}$ as ${m} X {n}$ matrices over $F_q$ by expanding each entry of the codeword with respect to an $F_q$ -basis of $F_{q^m}$, the rank weight of a codeword is the rank over $F_q$ of the corresponding matrix and the rank of the code is the minimum rank weight among all non-zero codewords. For ${m}\leq{n}-{k+1}$, codes with maximum possible rank distance, called maximum rank distance (MRD) codes have been studied previously. We study codes with maximum possible rank distance for the cases ${m}\leq{n}-{k+1}$, calling them full rank distance (FRD) codes. Generator matrices of FRD codes are characterized.

Item Type: Conference Paper Copyright 1990 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Division of Electrical Sciences > Electrical Communication Engineering 18 Jan 2006 19 Sep 2010 04:22 http://eprints.iisc.ernet.in/id/eprint/5143

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