Perfect Space–Time Block Codes

Perfect Space-Time Block Codes

Perfect Space Time Block Codes

Frédérique Oggier is with the California Institute of Technology, 91125 Pasadena, California, USA. When this work was done, she was with École Polytechnique Fédérale de Lausanne, 1015 Lausanne, SWITZERLAND Ghaya Rekaya and Jean-Claude Belfiore are with École Nationale Supérieure des Télécommunications, 46 rue Barrault, 75013 Paris, FRANCE Emanuele Viterbo is with Politecnico di Torino, C.so Duc...

Perfect Space-Time Block Codes and Ultra-Wideband

In this report, we present the techniques for constructing Space-Time Block Codes based on division algebra. Even though commutative division algebra can be applied for the construction, we focus on noncommutative division algebra, especially in the construction of so-called perfect space-time (ST) block codes. These codes provide full rate, full diversity and non-vanishing constant minimum det...

The (non-)existence of perfect codes in Lucas cubes

A Fibonacci string of length $n$ is a binary string $b = b_1b_2ldots b_n$ in which for every $1 leq i < n$, $b_icdot b_{i+1} = 0$. In other words, a Fibonacci string is a binary string without 11 as a substring. Similarly, a Lucas string is a Fibonacci string $b_1b_2ldots b_n$ that $b_1cdot b_n = 0$. For a natural number $ngeq1$, a Fibonacci cube of dimension $n$ is denoted by $Gamma_n$ and i...

No More Perfect Codes: Classification of Perfect Quantum Codes

We solve the problem of the classification of perfect quantum codes. We prove that the only nontrivial perfect quantum codes are those with the parameters ( ( 2 2 2 ( 1) ( 1) , ,3 l n q q q q − − − )) l . There exist no other nontrivial perfect quantum codes.