On (partial) unit memory codes based on Gabidulin codes
The authors consider unit memory and partial unit memory convolutional codes. These rank-\(k/n\) codes have memory 1 and overall constraint length \(\nu=k\) (unit memory codes) or \(\nu<k\) (partial unit memory codes). Thus a (partial) unit memory code has a \(k \times n\) generator matrix of polynomials of degree at most 1. Since the memory is 1, the generator matrix may be given in the form \(G_0+G_1\cdot D\) where \(G_0\), \(G_1\) are scalar matrices of size \(k \times n\). Upper bounds on the free rank distance and slope of unit memory and partial unit memory codes are given. The authors also give a construction for unit memory and partial unit memory codes based on Gabidulin codes, which are certain block codes defined in terms of a parity check matrix. This construction meets the free rank distance upper bound and reaches half of the slope upper bound.
scientific article; zbMATH DE number 6014354
scientific article