Good integers and some applications in coding theory
Good integers and some applications in coding theory
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DOI：
10.1007/s12095-017-0255-4
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发表时间：
2016-11
期刊：
影响因子：
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通讯作者：
Somphong Jitman
中科院分区：
文献类型：
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作者：
Somphong Jitman
P. Moree 于 1997 年提出了一类好整数以及好奇整数的表征。这些整数已被证明具有良好的数论性质和广泛的应用。在本文中，给出了所有好整数的完整表征。引入了好整数的两个子类，即奇好整数和偶好整数。确定了这两个子类中好整数的特征和性质。作为应用，好整数和奇好整数被应用于阿贝尔码外壳的研究。阿贝尔码外壳的平均尺寸与一些上限和下限一起给出。
A class of good integers has been introduced by P. Moree in 1997 together with the characterization of good odd integers. Such integers have shown to have nice number theoretical properties and wide applications. In this paper, a complete characterization of all good integers is given. Two subclasses of good integers are introduced, namely, oddly-good and evenly-good integers. The characterization and properties of good integers in these two subclasses are determined. As applications, good integers and oddly-good integers are applied in the study of the hulls of abelian codes. The average dimension of the hulls of abelian codes is given together with some upper and lower bounds.