几类有限环上的深度谱,MacWilliams恒等式肯自对偶码的研究.pdfVIP

Research On Depth spectra, M acwilliam s identity and Self-dual codes over Some classes of Finite Rings A bstract In the first part, the depth distraction and the depth spectra of linear codes over two types of ring Fp + vFp(v2 = v) and Fp + vFp + v 2Fp(v3 = v) are discussed. By using the two types of ring genera­ tor matrices of the codes and two special homomorphisms of Abelian groups, the special linear codes over Fp and their generator matrices are obtained. In the end prove to the following two results:( 1)The range of the depth spectra of linear codes over ring Fp + vFp of type p 2klpk2p k3 are obtained,the depth spectra at least k 1 + k2 + k3 nonzero value and up to 2k 1 + k2 + k3 nonzero value;(2)By using the relationship of f (C), g(C ), h(C ), the depth distribution and the depth spectrum of linear codes over Fp + vFp + v 2Fp are discussed, then the depth distri­ bution of a class of linear codes over Fp + vFp + v 2Fp is showed.So,if D is the depth spectra of linear codes C then k 1 + k2 + ... + k7 |D| k 1 + k2 + ... + k7+rank K. In the second part, By give the definition of the Gray map on Zp2 + uZp2 (u2 = u). MacWilliams identity for the complete Gray weight enumerator is studied.Moreover the properties of Self-dual codes over Zp2 + uZp2 is studied.Then,if C is a Euclidean self-dual code over Zp2 + uZp2, then Res(C) is a Euclidean self-orthogonal code over the ring Fp + uFp. Keywords: linear codes; the depth of a codeword; depth