【摘要】 文献[2]、[3]分别给出了Goppa码、Alternant码最小距离新下限。但是要求出它们的下限,都需要计算出若干个循环陪集。本文首先给出循环陪集首集A溉念,然后推出了求最小距离下限问题即是求A中第一个大于给定正整数r的元M(r)的问题。讨论了A与M(r)一系列特性,给出了一些情况下M(r)的统一公式,以及求M(r)的快速而简便的方法。通过本文讨论,求Goppa码、Alternant码最小距离下限问题得到了很大简化。此外,本文还简单地讨论了给定最小距离如何设计Goppa码、Alternant码的问题。更多还原

【Abstract】 Two new lower bounds on minimum distance for Goppa codes and for Alternant codes were proposed in [2] and [3] respectively. But the method of finding them is based on computing some cycloto-mic cosets. In this paper, the idea of the lead set A of cyclotomic cosets is first presented. Then it is derived that the problem of finding the two lower bounds is the problem of finding the element M(r) which is first greater than the given r in A. This paper discusses a series properties of A and M(r), and also gives some formulas of M(r) for some cases and a method of computing M(r) that is speedy and simple. The finding of the two lower bounds becomes easier by this paper. Moreover, the problem of designing Goppa codes and Alternant codes for a given minimum distance is simply discussed.更多还原