并元加集与二元并元码

Dyadic Addition Sets and Binary Dyadic Codes

本文首先进一步研究了并元加集存在的必要条件，从而提出了二元并元码所具有的长度。然后给出了一系列二元并元码的构造方法。证明了存在长度为２２ｔ＋２的二元并元码，相应地证明了存在参数为（２２ｔ＋２，２２ｔ＋１±２ｔ，２２ｔ±２ｔ）的并元加集。

Necessary conditions for the existence of dyadic addition sets and for the length of binary dyadic codes are presented. By our new constructions of dyadic codes, the existence of binary dyadic codes of length 2 2t+2 and dyadic addition sets with parameters (2 2t+2 ,2 2t+1 ±2 t ,2 2t ±2 t ), for any positive integer t is proved.