关键词: F2＋uF2 循环码 生成元 准素多项式

Abstract:

A cyclic code with length 2n（n is odd）is called a cyclic code with oddly even lengths. We prove that any cyclic code over F2 ＋uF2 with oddly even l engths has generators of the form （a1 （x^2 ）a3 （x^2 ）a4 （x^2 ）a5^ ～（x）a6 （x）, ua1 （x^2 ）a2 （x^2）a4 （x）a5 （x^2））, whereПi=1^6ai（x）=x^n-1,a5^  ～（x）≡a5（x）（modu）,and. the structure of its dual code has been given in this paper as well.

Key words: （F2 ＋uF2, cyclic code, generator, primary polynomial）