关于四元环上广义H-码的注记

A Note of Generalized H-Codes over Quaternary Rings

可交换的有单位元在四元环的同构意义下只有四个(即域 GF(4)、环 F_2+uF_2、F_2+uF_2和 Z_4),域 GF(4)、环 F_2+uF_2、和 F_2+uF_2上广义 H-码与自偶码或型Ⅱ码的判别法已经解决,本文利用代数方法证明了环 Z_4上不存在是自偶的广义H-码,同时给出 Z_4环上码字的 Euclidean 重量的线性关系式。

There are only 4 different quaternary commutative rings with identity：GF （4）,F2＋uF2.F2＋uF2 and Z4. The generalized H-code （GH-code）are solved which are type Ⅱ code over GF （4）, F2＋uF2, F2＋uF2 .In this paper, the existent problem for a GH-code to be a selfdual code or a type Ⅱ code is solved over Z4 by using algebric method.And the linear relating equation of Euclidean weight of codewords is presented over Z4.