Galois环GR(22, 22s)上的一类几乎差族
A Family of Almost Difference Family on Galois Ring GR(22, 22s)
摘要:
几乎差族在编码、通信安全等领域有着广泛的应用。本文利用Galois环GR(2
2, 2
2s)上一种不相交的差族，通过对差族中某个集合添加一个元素，当满足一定条件时，即可构造出GR(2
2, 2
2s)上的几乎差族。
Abstract:
The almost difference family has a wide range of applications in coding, communication security and other fields. This paper uses one family of disjoint difference family on Galois ring GR(22, 22s), and by adding an element to a set in the difference family, when certain conditions are met, a new family of almost difference family can be constructed.
参考文献
|
[1]
|
Wan, Z.X. (2003) Lectures on Finite Fields and Galois Rings. World Scientific Publishing Company, Singapore.
|
|
[2]
|
李锦. 伽罗华环上指数和及其在通信中的应用[D]: [博士学位论文]. 合肥: 合肥工业大学, 2014.
|
|
[3]
|
郑鹭亮, 林丽英. 基于6阶分圆数的广义几乎差集构造[J]. 龙岩学院学报, 2012, 30(5): 1-8.
|
|
[4]
|
刘永晴, 孔庆欣, 陆俞先, 汤静, 王天祎, 唐玲丽. 一些新的差族和几乎差族[J]. 应用数学进展, 2020, 9(3): 451-457.
|
|
[5]
|
Ray-Chaudhuri, D.K. and Xiang, Q. (1996) Constructions of Partial Difference Sets and Relative Difference Sets Using Galois Rings. Designs, Codes and Cryptography, 8, 215-227. [Google Scholar] [CrossRef]
|
|
[6]
|
Momihara, K. (2012) Note on Divisible Difference Sets from Galois Rings GR (9, n). arXiv preprint arXiv:1210.1278
|
|
[7]
|
Momihara, K. (2017) Disjoint Difference Families from Galois Rings. The Electronic Journal of Combinatorics, 24, 3-23. [Google Scholar] [CrossRef]
|
|
[8]
|
Ding, C.S. and Yuan, J. (2005) A Family of Skew Hadamard Difference Sets. Journal of Combinatorial Theory, Series A, 113, 1526-1535. [Google Scholar] [CrossRef]
|
|
[9]
|
Ding, C.S., Wang, Z.Y. and Xiang, Q. (2006) Skew Hadamard Difference Sets from the Ree-Tits Slice Symplectic Spreads in PG (3, 32h+1). Journal of Combinatorial Theory, Series A, 114, 867-887.
|