Full rank perfect codes and \(\alpha \)-kernels
There are few general constructions of full rank perfect codes, that are not given by recursive methods using perfect codes of length shorter than \(n= 2^m-1\). In this paper, the author constructs full rank perfect codes, the so-called normal \(\alpha\)-codes, by first finding the superdual of the perfect code. The kernel of such normal \(\alpha\)-codes have also been considered and it is proved that any subspace of the kernel of a normal \(\alpha\)-code that satisfies a certain property is the kernel of another perfect code of the same length \(n\). In this way, the author has been able to relate some of the full rank perfect codes of length \(n\) to other full rank perfect codes of the same length \(n\).
scientific article; zbMATH DE number 5566687
scientific article