Minimal Tail-Biting Trellises for Linear MIX Codes over $F_{p^m}$

摘要

For all linear (n,k,d) MDS codes over finite fields $F_{p^m}$ we identity a generator matrix with the property that the product of trellises of rows of the generator matrix will give a minimal tail-biting linear trellis, and viewing the code as a group code, identify a set of generators, the product of whose trellises will give a minimal tail biting group trellis. We also give the necessary and sufficient condition for the existence of flat minimal linear and group tail-biting trellises.