超立方体幂图中常重点集导出子图的一类独立集
A Class of Independent Sets of Subgraphs Derived from Constant Focus Sets in Hypercube Power Graphs
DOI: 10.12677/AAM.2022.113126, PDF,   
作者: 师娟娟, 杨卫华*：太原理工大学，数学学院，山西 晋中
关键词: 超立方体；最大独立集；常重码；Hypercube； Maximum Independent Set； Constant Weight Code
摘要: 编码理论中的一个基本问题是求A(n,d,w)的值，即长度为n，重量为w，最小Hamming距离为d的二元码集的大小。它可看作是n维超立方体 次幂图中所有重量为w的点导出子图Qn(d-1,w)的最大独立集。本文运用构造图Qn(d-1,w)的最大独立集的方法得到n、d和w为某些特殊值时，A(n,d,w)=4 。
Abstract: A basic problem in coding theory is to find the value of A(n,d,w), that is, the size of the maximum binary code with length n, constant weight w and minimum Hamming distance d. It can also be re-garded as the maximum independent set of induced subgraph of points of weight w of the th d-1th-power of n-dimensional hypercube Qn(d-1,w) . We use the method of constructing the maximum independent set of Qn(d-1,w) to obtain A(n,d,w)=4 for some special n, d and w.
文章引用：师娟娟, 杨卫华. 超立方体幂图中常重点集导出子图的一类独立集[J]. 应用数学进展, 2022, 11(3): 1170-1177. https://doi.org/10.12677/AAM.2022.113126

参考文献

[1] Kleitman, D.J. (1966) On a Combinatorial Conjecture of Erdös. Journal of Combinatorial Theory, 1, 1209-1214. [Google Scholar] [CrossRef] 
[2] Hamming, R.W. (1950) Error Detecting and error Correcting Codes. Bell System Technical Journal, 29, 147-160. [Google Scholar] [CrossRef] 
[3] Johnson, S.M. (1962) A New Upper Bound for Er-ror-Correcting Codes. IEEE Transactions on Information Theory, 8, 203-207. [Google Scholar] [CrossRef] 
[4] MacWilliams, F.J. and Sloane, N.J.A. (1977) The Theory of Er-ror-Correcting Codes. Elsevier, North-Holland.
[5] Agrell, E. and Vardy, A. (2000) Upper Bounds for Con-stant-Weight Codes. IEEE Transactions on Information Theory, 46, 2373-2395. [Google Scholar] [CrossRef] 
[6] Cornelis, L.M. and, Van, P. and Tuvi, E. (1989) New Lower Bounds for Constant Weight Codes. IEEE Transactions on Information Theory, 35, 1324-1329. [Google Scholar] [CrossRef] 
[7] Brouwer, A.E., Shearer, J.B., Sloane, N.J.A. and Smith, W.D. (1990) A New Table of Constant Weight Codes. IEEE Transactions on Information Theory, 36, 1334-1380. [Google Scholar] [CrossRef] 
[8] Johnson, S.M. (1971) On Upper Bounds for Unrestricted Binary Er-ror-Correcting Code. IEEE Transactions on Information Theory, 17, 466-478.
[9] Chee, Y.M., Xing, C. and Yeo, S.L. (2010) New Constant-Weight Codes from Propagation Rules. IEEE Transactions on Information Theory, 56, 1596-1599. [Google Scholar] [CrossRef] 
[10] Kang, B.G., Kim, H.K. and Toan, P.Y. (2012) Delsarte’s Linear Programming Bound for Constant-Weight Codes. IEEE Transactions on Information Theory, 58, 5956-5962. [Google Scholar] [CrossRef] 
[11] Schrijver, A. (2005) New Code upper Bounds from the Terwilliger Algebra and Semidefinite Programming. IEEE Transactions on Information Theory, 51, 2859-2866. [Google Scholar] [CrossRef] 
[12] Kibler, R.E. (1980) Some New Constant Weight Codes (Corresp.). IEEE Transactions on Information Theory, 26, 364-365. [Google Scholar] [CrossRef] 
[13] Ostergard, P.R.J. (2010) Classification of Binary Constant Weight Codes, IEEE Transactions on Information Theory, 56, 3779-3785. [Google Scholar] [CrossRef] 
[14] Lan, L., Chang, Y. and Wang, L. (2016) Cyclic Constant-Weight Codes: Upper Bounds and New Optimal Constructions. IEEE Transactions on Information Theory, 62, 6328-6341. [Google Scholar] [CrossRef] 
[15] 寇永芳, 吕梦欣, 胡晓敏, 杨卫华. 关于A(n,d,w)的一个注记, 应用数学进展, 2021, 10(3): 740-746. [Google Scholar] [CrossRef] 

为你推荐