| 利用有限域GF（2m）上的三项式构造二元循环码 |
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| 引用本文： | 张爱仙,冯克勤.利用有限域GF（2m）上的三项式构造二元循环码[J].纯粹数学与应用数学,2016,32(4):380-386. |
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| 作者姓名： | 张爱仙 冯克勤 |
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| 作者单位： | 西安理工大学数学系,陕西 西安,710048;清华大学数学系,北京,100084 |
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| 基金项目： | 国家自然科学基金(11401468 |
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| 摘 要： | 循环码是一类特殊的线性码,由于循环码快速的编码和译码算法,它被广泛应用于消费电子,数据存储以及通信系统当中.在本文中,利用特征是偶数的有限域上的三项式构造出了两类二元循环码,我们不仅可以确定出这两类循环码最小距离的下界,而且这两类循环码在参数的选取上非常的灵活.
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| 关 键 词： | 循环码 三项式 序列 有限域 |
Binary cyclic codes from trinomials over GF(2m) |
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| Zhang Aixian,Feng Keqin.Binary cyclic codes from trinomials over GF(2m)[J].Pure and Applied Mathematics,2016,32(4):380-386. |
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| Authors: | Zhang Aixian Feng Keqin |
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| Abstract: | Cyclic codes are a subclass of linear codes and have wide applications in consumer electronics, data storage systems, and communication systems since they have e?cient encoding and decoding algorithms. In this paper, some trinomials over finite fields with even characteristic are employed to construct two classws of binary cyclic codes. Lower bounds on the minimum weight of some cyclic codes are developed. The dimensions of the codes obtained in this paper are flexible. |
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| Keywords: | cyclic codes trinomial sequences finite fields |
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