Dualities for codes over finite Abelian groups

Quantum Error-Correction Codes on Abelian Groups

We prove a general form of bit flip formula for the quantum Fourier transform on finite abelian groups and use it to encode some general CSS codes on these groups.

Asymptotically Good Codes Over Non-Abelian Groups

In this paper, we show that good structured codes over non-Abelian groups do exist. Specifically, we construct codes over the smallest non-Abelian group D6 and show that the performance of these codes is superior to the performance of Abelian group codes of the same alphabet size. This promises the possibility of using non-Abelian codes for multi-terminal settings where the structure of the cod...

Matrices of Finite Abelian Groups, Finite Fourier Transform and Codes

Finite (or Discrete) Fourier Transforms (FFT) are essential tools in engineering disciplines based on signal transmission, which is the case in most of them. FFT are related with circulant matrices, which can be viewed as group matrices of cyclic groups. In this regard, we introduce a generalization of the previous investigations to the case of finite groups, abelian or not. We make clear the p...

An E cient Algorithm for Constructing Minimal Trellises for Codes over Finite Abelian Groups

We present an eecient algorithm for computing the minimal trellis for a group code over a nite Abelian group, given a generator matrix for the code. We also show how to compute a succinct representation of the minimal trellis for such a code, and present algorithms that use this information to eeciently compute local descriptions of the minimal trellis. This extends the work of Kschischang and ...

An Efficient Algorithm for Constructing Minimal Trellises for Codes over Finite Abelian Groups