形式幂级数环上的自对偶码

The Self-dual Codes over Formal Power Series Rings

形式幂级数环R_∞=F[[γ]]={sum from l=0 to a_lγ~l|a_l∈F}与有限链环R_i={a_0+a_1γ+…+a_(i-1)γ^(i-1)|a_i∈F}的码的投影与提升有密切关系.利用形式幂级数环R_∞上码C在有限链环R_i的投影码的自正交性与自对偶性来研究码C的自正交性与自对偶性,得到了两个有意义的结果.

The codes of formal power series rings R∞=F[[γ]]={∑t=0^∞ alγ^l｜al∈F} and finite chain ringsRi={a0＋a1γ＋…＋a（i-1）γ^i-1｜ai∈F} have close relationship in lifted and projection.In this paper,we study self-orthogonal codes and self-dual codes over formal power series rings R_∞by means of self-orthogonal codes and self-dual codes over finite chain rings R_i,and obtain two results.