MDS Self-Dual Codes over Large Prime Fields
MDS Self-Dual Codes over Large Prime Fields
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DOI：
10.1006/ffta.2002.0353
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发表时间：
2002-10
影响因子：
1
通讯作者：
S. Georgiou;C. Koukouvinos
中科院分区：
文献类型：
--
作者：
S. Georgiou;C. Koukouvinos
组合设计在自对偶码的构造中得到了广泛的应用。最近，利用正交设计建立了一种构造自对偶码的新方法。这种方法已导致许多新的自对偶码的建设小有限域和环。本文利用广义正交设计推广了这一方法，给出了GF（p）上的Diophantine方程的另一种新的构造和求解方法，以寻找合适的自对偶码的生成矩阵。我们表明，在必要的条件下，这些方法也可以适用于小型和大型领域。我们应用这两种方法研究了GF（31）和GF（37）上的自对偶码。利用这些方法，我们得到了一些新的小阶最大距离可分自对偶码。
Combinatorial designs have been used widely in the construction of self-dual codes. Recently a new method of constructing self-dual codes was established using orthogonal designs. This method has led to the construction of many new self-dual codes over small finite fields and rings. In this paper, we generalize this method by using generalized orthogonal designs, and we give another new method that creates and solves Diophantine equations over GF(p) in order to find suitable generator matrices for self-dual codes. We show that under the necessary conditions these methods can be applied as well to small and large fields. We apply these two methods to study self-dual codes over GF(31) and GF(37). Using these methods we obtain some new maximum distance separable self-dual codes of small orders.