The Structure And Application Of Generalized Quasi-twisted Code

Recently,coding theory over finite field has been one of the most important topic of coding theory.Based on the previous work,we study the structure of generalized quasi-twisted code and give a study on generator polynomial matrices and parity-check polynomial matrices of generalized quasi-twisted code.In Chapter 1,we mainly introduce the background and the related research of coding theory and generalized quasi-cyclic codes.In Chapter 2,we give their polynomial expression,convert from their generator matrices to generator polynomial matrices by Buchberger's algorithm and shows the existence of generator polynomial matrices,express generalized quasi-twisted code by generator polynomial matrices.In Chapter 3,we study the properties of generator polynomial matrices.Firstly,we given the identical equation from generator polynomial matrices and study their properties Secondly,we show a theorem to show calculate parity-check polynomial matrices.Furthermore,we also give a method of listing all generator polynomial matrices.In Chapter 4,we study the duality theory of generalized quasi-twisted code,We study the orthogonality in M,and show similar results for parity-check polynomial matrices,given a theorem to calculate generator polynomial matrices.