有限域上高斯正规基的一个注记

DOI: 10.3969/j.issn.1001-8395.2015.02.001, PP. 159-163

Keywords: 有限域,正规基,乘法表,复杂度,分圆数

Full-Text   Cite this paper   Add to My Lib

Abstract:

利用有限域和分圆数的性质,给出Fqn在Fq上7-型高斯正规基满足一定条件的等价刻画.

References

[1]	Anuradha S, Gurmeet K. Baksh. The weight distribution of some irreducible cyclic codes[J]. Finite Fields Their Appl,2012,18(1):144-159.
[2]	Christopolou M, Garefalakis T, Panario D, et al. Gauss periods as constructions of low complexity normal bases[J]. Des Codes Cryptogr,2012,62:43-62.
[3]	Ding C, Helleseth T. New generalized cyclotomy and its applications[J]. Finite Fields Their Appl,1998,4:140-166.
[4]	Ding C, Helleseth T. Generalized cyclotomic codes of length pe11… pett[C]// IEEE Trans Inform Theory,1999,45(2):467-474.
[5]	Gao S, Lenstra Jr H W. Optimal normal bases[J]. Des Codes Cryptogr,1992,2:315-323.
[6]	Gao S, Gathen J V Z, Panario D, et al. Algorithms for exponentiation in finite fields[J]. J Symbol Comput,2000,29:879-889.
[7]	Liao Q Y, Feng K Q. On the complexity of the normal basis via prime Gauss period over finite fields[J]. J Sys Sci Complexity,2009,22(3):395-406.
[8]	Mullin R, Onyszchuk I, Vanstone S, et al. Optimal normal bases in GF(pm)[J]. Discrete Appl Math,1988/1989,22:149-161.
[9]	Lidl R, Niederreiter H. Finite Fields[M]. Cambridge:Cambridge University Press,1987.
[10]	Lidl R, Niederreiter H. Finite Fields and Their Applications[M]. 2nd Ed. Cambrige:Cambrige University Press,1994.
[11]	Wassermann A. Konstruktion von normalbasen[J]. Bayreuther Math Scriften,1990,31:155-164.
[12]	李波,廖群英. 有限域上k -型高斯正规基的对偶基及其乘法表[J]. 四川师范大学学报:自然科学版,2013,36(6):824-829.
[13]	廖群英,李威,汤建钢,等. 有限域上与k-型高斯正规基相关的自对偶正规基[J]. 四川师范大学学报:自然科学版,2013,36(5):663-668.
[14]	李俊,黄琴,李波,等. 有限域上k -型高斯正规基及其对偶基[J]. 四川师范大学学报:自然科学版,2011,34(3):289-295.

Full-Text