二元叠加码M(m,k,d)的平均汉明距离和均方差
|
摘要
根据二元叠加码(Binary Superimposed Code)M(m,k,d)的定义及完全图K_(2m)的性质,研究了M(m,k,d)码的平均汉明(Hamming)距离和它的均方差问题,给出了它们的计算公式.
By definition of binary superimposed code M(m, k, d) and properties of complete graph K_(2m), the average Hamming distance and mean square deviation of binary superimposed code M(m, k, d) were studied. Their computational formulas are obtained.
By definition of binary superimposed code M(m, k, d) and properties of complete graph K_(2m), the average Hamming distance and mean square deviation of binary superimposed code M(m, k, d) were studied. Their computational formulas are obtained.
引文
[1] Ngo H Q, Du D Z. New constructions of non-adaptive and error-tolerance pooling designs[J]. Discrete Mathematics, 2002, 243:161-170.
[2]高建平,邓超公.二元码Mq(n,k,d)的检错性和纠错性[J].数学的实践与认识,2015, 45(14):319-322.
[3]闫常丽,温新苗,王利民.二元叠加码M_q(n,k,d)的线性性质[J].数学的实践与认识,2016, 46(14):293-296.
[4]李晓东,温新苗,韩桂玲.一类二元容错码的扩展和算法[J].数学的实践与认识,2016, 46(12):288-291.
[5]徐峰,霍丽芳,李晓东.二元叠加码M_q~c(n,k,d)的性质[J].数学的实践与认识,2016, 46(13):293-296.
[6]夏树涛,符方伟.二元码的平均Hamming距离和方差[J].数学物理学报,1999,19(4):368-372.
[7] Althofer I, Sillke T. An average distance inequality for large subsets of the cube[J]. Journal of Combinatorial Theory, Series B, 1992, 56:296-301.
[8]魏会贤,胡海燕.二元叠加码M_q(n,k,d)码的平均汉明距离和均方差[J].数学的实践与认识,2017,47(6):292-296.
[9] Du Dingzhu, Hwang F K. Combinatorial Group Testing and Its Applications[M]. World Scientific,Singapore, 2000.
[10] Du D Z, Hwang F K. Pooling Designs and Nonadaptive Group Testing[M]. Word Scientific, Singepore, 2006.
[11] Mahdi C. Improved constructions for non-adaptive threshold group testing[J]. Algorithmica, 2013,67:384-417.
[12] D'yachkov A,Rykov V,Deppe C, Lebedev V. Superimposed codes and threshold group testing[J].Lecture Notes in Computer Science, 2013, 7777:509-533.
[13] Wang Kaishun, Guo Jun, Li Fenggao. Association schemes based on attenuated spaces[J]. European Journal of Combinatorics, 2010, 31:297-305.
[14] West D B.著,李建中,骆吉州译.图论导引[M].机械工业出版社(第二版),北京,2006.
[15]吴琼扬,霍丽芳.二元叠加码δ(n,d,k)的平均汉明距离和均方差[J].数学的实践与认识,2018, 48(14):251-255.
[2]高建平,邓超公.二元码Mq(n,k,d)的检错性和纠错性[J].数学的实践与认识,2015, 45(14):319-322.
[3]闫常丽,温新苗,王利民.二元叠加码M_q(n,k,d)的线性性质[J].数学的实践与认识,2016, 46(14):293-296.
[4]李晓东,温新苗,韩桂玲.一类二元容错码的扩展和算法[J].数学的实践与认识,2016, 46(12):288-291.
[5]徐峰,霍丽芳,李晓东.二元叠加码M_q~c(n,k,d)的性质[J].数学的实践与认识,2016, 46(13):293-296.
[6]夏树涛,符方伟.二元码的平均Hamming距离和方差[J].数学物理学报,1999,19(4):368-372.
[7] Althofer I, Sillke T. An average distance inequality for large subsets of the cube[J]. Journal of Combinatorial Theory, Series B, 1992, 56:296-301.
[8]魏会贤,胡海燕.二元叠加码M_q(n,k,d)码的平均汉明距离和均方差[J].数学的实践与认识,2017,47(6):292-296.
[9] Du Dingzhu, Hwang F K. Combinatorial Group Testing and Its Applications[M]. World Scientific,Singapore, 2000.
[10] Du D Z, Hwang F K. Pooling Designs and Nonadaptive Group Testing[M]. Word Scientific, Singepore, 2006.
[11] Mahdi C. Improved constructions for non-adaptive threshold group testing[J]. Algorithmica, 2013,67:384-417.
[12] D'yachkov A,Rykov V,Deppe C, Lebedev V. Superimposed codes and threshold group testing[J].Lecture Notes in Computer Science, 2013, 7777:509-533.
[13] Wang Kaishun, Guo Jun, Li Fenggao. Association schemes based on attenuated spaces[J]. European Journal of Combinatorics, 2010, 31:297-305.
[14] West D B.著,李建中,骆吉州译.图论导引[M].机械工业出版社(第二版),北京,2006.
[15]吴琼扬,霍丽芳.二元叠加码δ(n,d,k)的平均汉明距离和均方差[J].数学的实践与认识,2018, 48(14):251-255.