环Z_4上一些线性码的深度谱

Study of the depth spectrum of some linear codes on the ring Z_4

文章主要研究环Z4上线性码的深度谱,证明了2k型的线性码的深度谱恰含有k个非零值;从4k12k2型线性码的2k型子码与有限域F2上线性码的同构关系出发,对于一般的4k12k2型线性码的深度谱进行了分析;给出了一些满足特定条件的线性码的深度谱。

It is proved in the paper that the depth spectrum of linear codes of the type 2^k over the ring Z4 consists exactly of k nonzero values. In addition, in light of the isomorphism between the linear subcodes of the type 2^k and the linear codes over the Galois field F2, the property of the depth spectrum of linear codes of the type 4^k12^k2 is researched, and the depth spectrum of some linear codes which fulfill certain specific conditions is given.