MacWilliams Identities of Linear Codes Over Ring F_2+uF_2+u~2F_2
Liang Hua, Yuansheng Tang · Shuxue de shijian yu renshi · 2010
LetR=F_2+uF_2+u~2F_2,Lee Weight distribution of linear codes over R is defined and the Gray mapφ from R~n to F_2~(3n) is constructed.By studying the generator matrices of linear codes and their dual codes over R,it is proved that the Gray image of linear codes and their dual codes over R are dual codes over F2.Based on the relationship of linear codes and their dual codes over F_2,the MacWilliams identities for Lee weight distribution of the linear codes over R and their dual codes are obtained.