求Alternant码最小距离下界

An approach to the lower bound on minimum distance for Alternant codes

陈克非给出了Ａｌｔｅｒｎａｎｔ码最小距离新下界，但要具体求出这个下界，需要进行有限域上求解共扼元集合的复杂运算。为了避免这个复杂运算过程，给出了循环陪集一个特性，并利用这一特性导出了这个下界新的表示定理，运用表示定理求解下界运算得到了很大简化。文中还给出了一定情况下求下界的统一公式。

A new lower bound on minimum distance for Alternant codes was propo- sed by Chen Kefei. But the method of finding it is based on finding some sets of conjugate elememts in a finite, which is usually very complicated. In this paper, a property of cyclotomic cosets is discussed. A theorem of the lower bound is derived from the property, and the finding of the lower bound becomes easier with the theorem. Moreover, a new formula for the lower bound is offered for some cases.