On Four-negacirculant Self-Dual Code Over Some Prime Fields

The application of digital communication is becoming more and more popular; the change of information's transmission way is developing deeply; and the number of data in sending process is being increased rapidly. In this situation, how to reduce and correct mistakes in transmittal process is becoming more and more urgent.So it has very impor-tant meaning in the study of coding theory. And the particularity of self-dual codes makes the research on them having largely academic value,and it has also been wildly applied in practices.In this paper,we construct some self-dual codes under a new inner product (extended involution) based on negacirculant matrixes.A classification of such codes is given and the largest minimum weights of these codes are investigated.In this method we can construct optimal self-dual codes,i.e maximum distance separable (MDS) codes.