doi: 10.3934/amc.2022008
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

Balanced ($\mathbb{Z} _{2u}\times \mathbb{Z}_{38v}$, {3, 4, 5}, 1) difference packings and related codes

1. 

Department of Mathematics and Information Science, Guangxi College of Education, Nanning 530023, China

2. 

Department of Mathematics, Guangxi Agricultural Vocational University, Nanning 530007, China

3. 

School of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China

*Corresponding author: Dianhua Wu

Received  September 2021 Revised  January 2022 Early access February 2022

Fund Project: The first author is supported by BAGUI Scholar Program of Guangxi Zhuang Autonomous Region of China (No. 201979). The second author is supported in part by Guangxi Nature Science Foundation (No. 2019GXNSFBA245021), and the Project of Basic Ability Improvement of Young and Middle-aged Teachers of Universities in Guangxi (No. 2020KY54014). The last author is supported in part by NSFC (No. 12161010, 11801103)

Let $ m $, $ n $ be positive integers, and $ K $ a set of positive integers with size greater than 2. An $ (m,n,K,1) $ optical orthogonal signature pattern code, $ (m,n,K,1) $-OOSPC, was introduced by Kwong and Yang for 2-D image transmission in multicore-fiber optical code-division multiple-access (OCDMA) networks with multiple quality of services (QoS) requirement. Let $ G $ be an additive group, a balanced $ (G, K, 1) $ difference packing, $ (G, K, 1) $-BDP, can be used to construct a balanced $ (m,n,K,1) $-OOSPC when $ G = {\mathbb{Z}}_m\times {\mathbb{Z}}_n $. In this paper, the existences of optimal $ ( {\mathbb{Z}}_{2u}\times {\mathbb{Z}}_{38v}, \{3,4,5\},1) $-BDPs are completely solved with $ u, \ v\equiv 1\pmod2 $, and the corresponding optimal balanced $ (2u, 38v,\{3,4,5\},1) $-OOSPCs are also obtained.

Citation: Hengming Zhao, Rongcun Qin, Dianhua Wu. Balanced ($\mathbb{Z} _{2u}\times \mathbb{Z}_{38v}$, {3, 4, 5}, 1) difference packings and related codes. Advances in Mathematics of Communications, doi: 10.3934/amc.2022008
References:
[1]

R. J. R. Abel, C. J. Colbourn and J. H. Dinitz, Mutually orthogonal latin squares (MOLS), Handbook of Combinatorial Designs, New York: CRC Press, (2007), 160–193.

[2]

S. BonviciniM. BurattiM. Garonzi and G. Traetta, The first families of highly symmetric Kirkman triple systems whose orders fill a congruence class, Designs, Codes and Cryptography, 89 (2021), 2725-2757.  doi: 10.1007/s10623-021-00952-x.

[3]

M. Buratti, A power method for constructing difference families and optimal optical orthogonal codes, Des. Codes Cryptogr., 5 (1995), 13-25.  doi: 10.1007/BF01388501.

[4]

M. Buratti, Hadamard partitioned difference families and their descendants, Cryptogr. Commun., 11 (2019), 557-562.  doi: 10.1007/s12095-018-0308-3.

[5]

M. Buratti, Old and new designs via difference multisets and strong difference families, J. Combin. Des., 7 (1999), 406-425.  doi: 10.1002/(SICI)1520-6610(1999)7:6<406::AID-JCD2>3.0.CO;2-U.

[6]

M. Buratti, On silver and golden optical orthogonal codes, Art Discrete Appl. Math., 1 (2018), Paper No. 2.02, 11 pp. doi: 10.26493/2590-9770.1236. ce4.

[7]

M. Buratti, Recursive constructions for difference matrices and relative difference families, J. Combin. Des., 6 (1998), 165-182.  doi: 10.1002/(SICI)1520-6610(1998)6:3<165::AID-JCD1>3.0.CO;2-D.

[8]

M. BurattiY. WeiD. WuP. Fan and M. Cheng, Relative difference families with variable block sizes and their related OOCs, IEEE Trans. Inform. Theory, 57 (2011), 7489-7497.  doi: 10.1109/TIT.2011.2162225.

[9]

M. Buratti, J. Yan and C. Wang, From a 1-rotational RBIBD to a partitioned difference family, Electron. J. Combin., 17 (2010), 139, 23 pp.

[10]

M. Buratti and F. Zuanni, G-Invariantly resolvable Steiner 2-designs arising from 1-rotational difference families, Bull. Belg. Math. Soc., 5 (1998), 221-235. 

[11]

Y. Chang, S. Costa, T. Feng and X. Wang, Strong difference families of special types, Discr. Math., 343 (2020), 111776, 12 pp. doi: 10.1016/j. disc. 2019.111776.

[12]

K. ChenG. Ge and L. Zhu, Starters and related codes, J. Statist. Plann. Inference, 86 (2000), 379-395.  doi: 10.1016/S0378-3758(99)00119-6.

[13]

J. ChenL. Ji and Y. Li, Combinatorial constructions of optimal $(m, n, 4, 2)$ optical orthogonal signature pattern codes, Des. Codes Cryptogr., 86 (2018), 1499-1525.  doi: 10.1007/s10623-017-0409-6.

[14]

J. ChenL. Ji and Y. Li, New optical orthogonal signature pattern codes with maximum collision parameter 2 and weight 4, Des. Codes Cryptogr., 85 (2017), 299-318.  doi: 10.1007/s10623-016-0310-8.

[15]

C. J. Colbourn, Difference matrices, In: C. J. Colbourn, J. H. Dinitz, eds. CRC Handbook of Combinatorial Designs, New York: CRC Press, (2007), 411–419.

[16]

S. CostaT. Feng and X. Wang, Frame difference families and resolvable balanced incomplete block designs, Des. Codes Cryptogr., 86 (2018), 2725-2745.  doi: 10.1007/s10623-018-0472-7.

[17]

S. CostaT. Feng and X. Wang, New 2-designs from strong difference families, Finite Fields Appl., 50 (2018), 391-405.  doi: 10.1016/j.ffa.2017.12.011.

[18]

I. B. DjordjevicB. Vasic and J. Rorison, Design of multiweight unipolar codes for multimedia optical CDMA applications based on pairwise balanced designs, J. Lightw. Technol., 21 (2003), 1850-1856.  doi: 10.1109/JLT.2003.816819.

[19]

G. Ge, On $(g, 4;1)$-diffference matrices, Discr. Math., 301 (2005), 164-174.  doi: 10.1016/j.disc.2005.07.004.

[20]

G. Ge and J. Yin, Constructions for optimal $(v, 4, 1)$ optical orthogonal codes, IEEE Trans. Inform. Theory, 47 (2001), 2998-3004.  doi: 10.1109/18.959278.

[21]

F. R. Gu and J. Wu, Construction and performance analysis of variable-weight optical orthogonal codes for asynchronous optical CDMA systems, J. Lightw. Technol., 23 (2005), 740-748.  doi: 10.1109/JLT.2004.838880.

[22]

L. JiB. DingX. Wang and G. Ge, Asymptotically optimal optical orthogonal signature pattern codes, IEEE Trans. Inform. Theory, 64 (2018), 5419-5431.  doi: 10.1109/TIT.2017.2787593.

[23]

J. JiangD. Wu and M. H. Lee, Some infinte classes of optimal $(v, \{3, 4\}, 1, Q)$-OOCs with $Q\in\{\{1/3, 2/3\}, \{2/3, 1/3\}\}$, Graphs Combin., 29 (2013), 1795-1811.  doi: 10.1007/s00373-012-1235-2.

[24]

K. Kitayama, Novel spatial spread spectrum based fiber optic CDMA networks for image transmission, IEEE J. Select. Areas Commun., 12 (1994), 762-772.  doi: 10.1109/49.286683.

[25]

W. C. Kwong and G. C. Yang, Double-weight signature pattern codes for multicore-fiber code-division multiple-access networks, IEEE Commun. Lett., 5 (2001), 203-205.  doi: 10.1109/4234.922760.

[26]

W. LiH. ZhaoR. Qin and D. Wu, Constructions of optimal balanced $(m, n, \{4, 5\}, 1)$-OOSPCs, Adv. Math. Commun., 13 (2019), 329-341.  doi: 10.3934/amc.2019022.

[27]

S. Ma and Y. Chang, A new class of optimal optical orthogonal codes with weight five, IEEE Trans. Inform. Theory, 50 (2004), 1848-1850.  doi: 10.1109/TIT.2004.831845.

[28]

K. Momihara, Strong difference families, difference covers, and their applications for relative difference families, Des. Codes Cryptogr., 51 (2009), 253-273.  doi: 10.1007/s10623-008-9259-6.

[29]

R. Pan and Y. Chang, Combinatorial constructions for maximum optical orthogonal signature pattern codes, Discr. Math., 313 (2013), 2918-2931.  doi: 10.1016/j.disc.2013.09.005.

[30]

R. Pan and Y. Chang, Determination of the sizes of optimal $(m, n, k, \lambda, k-1)$-OOSPCs for $\lambda=k-1, k$, Discr. Math., 313 (2013), 1327-1337.  doi: 10.1016/j.disc.2013.02.019.

[31]

R. Pan and Y. Chang, Further results on optimal $(m, n, 4, 1)$ optical orthogonal signature pattern codes (in Chinese), Sci. Sin. Math., 44 (2014), 1141-1152. 

[32]

R. Pan and Y. Chang, $(m, n, 3, 1)$ optical orthogonal signature pattern codes with maximum possible size, IEEE Trans. Inform. Theory, 61 (2015), 1139-1148.  doi: 10.1109/TIT.2014.2381259.

[33]

R. Qin and H. Zhao, Constructions for optimal $(u\times v, \{3, 4\}, 1, Q)$-OOSPCs, Discr. Math., 342 (2019), 1924-1948.  doi: 10.1016/j.disc.2019.03.006.

[34]

J. A. Salehi, Emerging optical code-division multiple access communications systems, IEEE Network, 3 (1989), 31-39.  doi: 10.1109/65.21908.

[35]

M. Sawa, Optical orthogonal signature pattern codes with maximum collision parameter 2 and weight 4, IEEE Trans. Inform. Theory, 56 (2010), 3613-3620.  doi: 10.1109/TIT.2010.2048487.

[36]

M. Sawa and S. Kageyama, Optimal optical orthogonal signature pattern codes of weight 3, Biom. Lett., 46 (2009), 89-102. 

[37]

X. WangT. Feng and S. Wang, Existence of strong difference families and constructions for eight new $2$-designs, J. Combin. Des., 29 (2021), 225-242.  doi: 10.1002/jcd.21765.

[38]

D. WuH. ZhaoP. Fan and S. Shinohara, Optimal variable-weight optical orthogonal codes via difference packings, IEEE Trans. Inform. Theory, 56 (2010), 4053-4060.  doi: 10.1109/TIT.2010.2050927.

[39]

G. C. Yang, Variable-weight optical orthogonal codes for CDMA networks with multiple performance requirements, IEEE Trans. Commun., 44 (1996), 47-55. 

[40]

G. C. Yang and W. C. Kwong, Two-dimensional spatial signature patterns, IEEE Trans. Commun., 44 (1996), 184-191. 

[41]

J. Yin, A general construction for optimal cyclic packing designs, J. Combin. Theory (Ser. A), 97 (2002), 272-284.  doi: 10.1006/jcta.2001.3215.

[42]

J. Yin, Some combinatorial constructions for optical orthogonal codes, Discr. Math., 185 (1998), 201-219.  doi: 10.1016/S0012-365X(97)00172-6.

[43]

H. Zhao, On balanced optimal $(18u, \{3, 4\}, 1)$ optical orthogonal codes, J. Combin. Des., 20 (2012), 290-303.  doi: 10.1002/jcd.21303.

[44]

H. Zhao and R. Qin, Combinatorial constructions for optimal multiple-weight optical orthogonal signature pattern codes, Discr. Math., 339 (2016), 179-193.  doi: 10.1016/j.disc.2015.08.005.

[45]

H. Zhao, R. Qin and D. Wu, On balanced $({\mathbb{Z}}_4u\times {\mathbb{Z}}_8v, \{4, 5\}, 1)$ difference packings, Discr. Math., 344 (2021), 112552, 13 pp. doi: 10.1016/j. disc. 2021.112552.

[46]

H. ZhaoD. Wu and P. Fan, Constructions of optimal variable-weight optical orthogonal codes, J. Combin. Des., 18 (2010), 274-291.  doi: 10.1002/jcd.20246.

show all references

References:
[1]

R. J. R. Abel, C. J. Colbourn and J. H. Dinitz, Mutually orthogonal latin squares (MOLS), Handbook of Combinatorial Designs, New York: CRC Press, (2007), 160–193.

[2]

S. BonviciniM. BurattiM. Garonzi and G. Traetta, The first families of highly symmetric Kirkman triple systems whose orders fill a congruence class, Designs, Codes and Cryptography, 89 (2021), 2725-2757.  doi: 10.1007/s10623-021-00952-x.

[3]

M. Buratti, A power method for constructing difference families and optimal optical orthogonal codes, Des. Codes Cryptogr., 5 (1995), 13-25.  doi: 10.1007/BF01388501.

[4]

M. Buratti, Hadamard partitioned difference families and their descendants, Cryptogr. Commun., 11 (2019), 557-562.  doi: 10.1007/s12095-018-0308-3.

[5]

M. Buratti, Old and new designs via difference multisets and strong difference families, J. Combin. Des., 7 (1999), 406-425.  doi: 10.1002/(SICI)1520-6610(1999)7:6<406::AID-JCD2>3.0.CO;2-U.

[6]

M. Buratti, On silver and golden optical orthogonal codes, Art Discrete Appl. Math., 1 (2018), Paper No. 2.02, 11 pp. doi: 10.26493/2590-9770.1236. ce4.

[7]

M. Buratti, Recursive constructions for difference matrices and relative difference families, J. Combin. Des., 6 (1998), 165-182.  doi: 10.1002/(SICI)1520-6610(1998)6:3<165::AID-JCD1>3.0.CO;2-D.

[8]

M. BurattiY. WeiD. WuP. Fan and M. Cheng, Relative difference families with variable block sizes and their related OOCs, IEEE Trans. Inform. Theory, 57 (2011), 7489-7497.  doi: 10.1109/TIT.2011.2162225.

[9]

M. Buratti, J. Yan and C. Wang, From a 1-rotational RBIBD to a partitioned difference family, Electron. J. Combin., 17 (2010), 139, 23 pp.

[10]

M. Buratti and F. Zuanni, G-Invariantly resolvable Steiner 2-designs arising from 1-rotational difference families, Bull. Belg. Math. Soc., 5 (1998), 221-235. 

[11]

Y. Chang, S. Costa, T. Feng and X. Wang, Strong difference families of special types, Discr. Math., 343 (2020), 111776, 12 pp. doi: 10.1016/j. disc. 2019.111776.

[12]

K. ChenG. Ge and L. Zhu, Starters and related codes, J. Statist. Plann. Inference, 86 (2000), 379-395.  doi: 10.1016/S0378-3758(99)00119-6.

[13]

J. ChenL. Ji and Y. Li, Combinatorial constructions of optimal $(m, n, 4, 2)$ optical orthogonal signature pattern codes, Des. Codes Cryptogr., 86 (2018), 1499-1525.  doi: 10.1007/s10623-017-0409-6.

[14]

J. ChenL. Ji and Y. Li, New optical orthogonal signature pattern codes with maximum collision parameter 2 and weight 4, Des. Codes Cryptogr., 85 (2017), 299-318.  doi: 10.1007/s10623-016-0310-8.

[15]

C. J. Colbourn, Difference matrices, In: C. J. Colbourn, J. H. Dinitz, eds. CRC Handbook of Combinatorial Designs, New York: CRC Press, (2007), 411–419.

[16]

S. CostaT. Feng and X. Wang, Frame difference families and resolvable balanced incomplete block designs, Des. Codes Cryptogr., 86 (2018), 2725-2745.  doi: 10.1007/s10623-018-0472-7.

[17]

S. CostaT. Feng and X. Wang, New 2-designs from strong difference families, Finite Fields Appl., 50 (2018), 391-405.  doi: 10.1016/j.ffa.2017.12.011.

[18]

I. B. DjordjevicB. Vasic and J. Rorison, Design of multiweight unipolar codes for multimedia optical CDMA applications based on pairwise balanced designs, J. Lightw. Technol., 21 (2003), 1850-1856.  doi: 10.1109/JLT.2003.816819.

[19]

G. Ge, On $(g, 4;1)$-diffference matrices, Discr. Math., 301 (2005), 164-174.  doi: 10.1016/j.disc.2005.07.004.

[20]

G. Ge and J. Yin, Constructions for optimal $(v, 4, 1)$ optical orthogonal codes, IEEE Trans. Inform. Theory, 47 (2001), 2998-3004.  doi: 10.1109/18.959278.

[21]

F. R. Gu and J. Wu, Construction and performance analysis of variable-weight optical orthogonal codes for asynchronous optical CDMA systems, J. Lightw. Technol., 23 (2005), 740-748.  doi: 10.1109/JLT.2004.838880.

[22]

L. JiB. DingX. Wang and G. Ge, Asymptotically optimal optical orthogonal signature pattern codes, IEEE Trans. Inform. Theory, 64 (2018), 5419-5431.  doi: 10.1109/TIT.2017.2787593.

[23]

J. JiangD. Wu and M. H. Lee, Some infinte classes of optimal $(v, \{3, 4\}, 1, Q)$-OOCs with $Q\in\{\{1/3, 2/3\}, \{2/3, 1/3\}\}$, Graphs Combin., 29 (2013), 1795-1811.  doi: 10.1007/s00373-012-1235-2.

[24]

K. Kitayama, Novel spatial spread spectrum based fiber optic CDMA networks for image transmission, IEEE J. Select. Areas Commun., 12 (1994), 762-772.  doi: 10.1109/49.286683.

[25]

W. C. Kwong and G. C. Yang, Double-weight signature pattern codes for multicore-fiber code-division multiple-access networks, IEEE Commun. Lett., 5 (2001), 203-205.  doi: 10.1109/4234.922760.

[26]

W. LiH. ZhaoR. Qin and D. Wu, Constructions of optimal balanced $(m, n, \{4, 5\}, 1)$-OOSPCs, Adv. Math. Commun., 13 (2019), 329-341.  doi: 10.3934/amc.2019022.

[27]

S. Ma and Y. Chang, A new class of optimal optical orthogonal codes with weight five, IEEE Trans. Inform. Theory, 50 (2004), 1848-1850.  doi: 10.1109/TIT.2004.831845.

[28]

K. Momihara, Strong difference families, difference covers, and their applications for relative difference families, Des. Codes Cryptogr., 51 (2009), 253-273.  doi: 10.1007/s10623-008-9259-6.

[29]

R. Pan and Y. Chang, Combinatorial constructions for maximum optical orthogonal signature pattern codes, Discr. Math., 313 (2013), 2918-2931.  doi: 10.1016/j.disc.2013.09.005.

[30]

R. Pan and Y. Chang, Determination of the sizes of optimal $(m, n, k, \lambda, k-1)$-OOSPCs for $\lambda=k-1, k$, Discr. Math., 313 (2013), 1327-1337.  doi: 10.1016/j.disc.2013.02.019.

[31]

R. Pan and Y. Chang, Further results on optimal $(m, n, 4, 1)$ optical orthogonal signature pattern codes (in Chinese), Sci. Sin. Math., 44 (2014), 1141-1152. 

[32]

R. Pan and Y. Chang, $(m, n, 3, 1)$ optical orthogonal signature pattern codes with maximum possible size, IEEE Trans. Inform. Theory, 61 (2015), 1139-1148.  doi: 10.1109/TIT.2014.2381259.

[33]

R. Qin and H. Zhao, Constructions for optimal $(u\times v, \{3, 4\}, 1, Q)$-OOSPCs, Discr. Math., 342 (2019), 1924-1948.  doi: 10.1016/j.disc.2019.03.006.

[34]

J. A. Salehi, Emerging optical code-division multiple access communications systems, IEEE Network, 3 (1989), 31-39.  doi: 10.1109/65.21908.

[35]

M. Sawa, Optical orthogonal signature pattern codes with maximum collision parameter 2 and weight 4, IEEE Trans. Inform. Theory, 56 (2010), 3613-3620.  doi: 10.1109/TIT.2010.2048487.

[36]

M. Sawa and S. Kageyama, Optimal optical orthogonal signature pattern codes of weight 3, Biom. Lett., 46 (2009), 89-102. 

[37]

X. WangT. Feng and S. Wang, Existence of strong difference families and constructions for eight new $2$-designs, J. Combin. Des., 29 (2021), 225-242.  doi: 10.1002/jcd.21765.

[38]

D. WuH. ZhaoP. Fan and S. Shinohara, Optimal variable-weight optical orthogonal codes via difference packings, IEEE Trans. Inform. Theory, 56 (2010), 4053-4060.  doi: 10.1109/TIT.2010.2050927.

[39]

G. C. Yang, Variable-weight optical orthogonal codes for CDMA networks with multiple performance requirements, IEEE Trans. Commun., 44 (1996), 47-55. 

[40]

G. C. Yang and W. C. Kwong, Two-dimensional spatial signature patterns, IEEE Trans. Commun., 44 (1996), 184-191. 

[41]

J. Yin, A general construction for optimal cyclic packing designs, J. Combin. Theory (Ser. A), 97 (2002), 272-284.  doi: 10.1006/jcta.2001.3215.

[42]

J. Yin, Some combinatorial constructions for optical orthogonal codes, Discr. Math., 185 (1998), 201-219.  doi: 10.1016/S0012-365X(97)00172-6.

[43]

H. Zhao, On balanced optimal $(18u, \{3, 4\}, 1)$ optical orthogonal codes, J. Combin. Des., 20 (2012), 290-303.  doi: 10.1002/jcd.21303.

[44]

H. Zhao and R. Qin, Combinatorial constructions for optimal multiple-weight optical orthogonal signature pattern codes, Discr. Math., 339 (2016), 179-193.  doi: 10.1016/j.disc.2015.08.005.

[45]

H. Zhao, R. Qin and D. Wu, On balanced $({\mathbb{Z}}_4u\times {\mathbb{Z}}_8v, \{4, 5\}, 1)$ difference packings, Discr. Math., 344 (2021), 112552, 13 pp. doi: 10.1016/j. disc. 2021.112552.

[46]

H. ZhaoD. Wu and P. Fan, Constructions of optimal variable-weight optical orthogonal codes, J. Combin. Des., 18 (2010), 274-291.  doi: 10.1002/jcd.20246.

[1]

Qi Wang, Yue Zhou. Sets of zero-difference balanced functions and their applications. Advances in Mathematics of Communications, 2014, 8 (1) : 83-101. doi: 10.3934/amc.2014.8.83

[2]

Emma Hoarau, Claire david@lmm.jussieu.fr David, Pierre Sagaut, Thiên-Hiêp Lê. Lie group study of finite difference schemes. Conference Publications, 2007, 2007 (Special) : 495-505. doi: 10.3934/proc.2007.2007.495

[3]

Yang Yang, Xiaohu Tang, Guang Gong. New almost perfect, odd perfect, and perfect sequences from difference balanced functions with d-form property. Advances in Mathematics of Communications, 2017, 11 (1) : 67-76. doi: 10.3934/amc.2017002

[4]

Huiyuan Guo, Quan Yu, Xinzhen Zhang, Lulu Cheng. Low rank matrix minimization with a truncated difference of nuclear norm and Frobenius norm regularization. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022045

[5]

Cuiling Fan, Koji Momihara. Unified combinatorial constructions of optimal optical orthogonal codes. Advances in Mathematics of Communications, 2014, 8 (1) : 53-66. doi: 10.3934/amc.2014.8.53

[6]

T. L. Alderson, K. E. Mellinger. Geometric constructions of optimal optical orthogonal codes. Advances in Mathematics of Communications, 2008, 2 (4) : 451-467. doi: 10.3934/amc.2008.2.451

[7]

K. T. Arasu, Manil T. Mohan. Optimization problems with orthogonal matrix constraints. Numerical Algebra, Control and Optimization, 2018, 8 (4) : 413-440. doi: 10.3934/naco.2018026

[8]

Boris P. Belinskiy. Optimal design of an optical length of a rod with the given mass. Conference Publications, 2007, 2007 (Special) : 85-91. doi: 10.3934/proc.2007.2007.85

[9]

John A. D. Appleby, Xuerong Mao, Alexandra Rodkina. On stochastic stabilization of difference equations. Discrete and Continuous Dynamical Systems, 2006, 15 (3) : 843-857. doi: 10.3934/dcds.2006.15.843

[10]

Guoliang Zhang, Shaoqin Zheng, Tao Xiong. A conservative semi-Lagrangian finite difference WENO scheme based on exponential integrator for one-dimensional scalar nonlinear hyperbolic equations. Electronic Research Archive, 2021, 29 (1) : 1819-1839. doi: 10.3934/era.2020093

[11]

Meenakshi Kansal, Ratna Dutta, Sourav Mukhopadhyay. Group signature from lattices preserving forward security in dynamic setting. Advances in Mathematics of Communications, 2020, 14 (4) : 535-553. doi: 10.3934/amc.2020027

[12]

Jie Xu, Lanjun Dang. An efficient RFID anonymous batch authentication protocol based on group signature. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1489-1500. doi: 10.3934/dcdss.2019102

[13]

Yuxing Yang, Yanxun Chang, Lidong Wang. Kite-group divisible packings and coverings with any minimum leave and minimum excess. Advances in Mathematics of Communications, 2022  doi: 10.3934/amc.2022040

[14]

Anna Cima, Armengol Gasull, Francesc Mañosas. Global linearization of periodic difference equations. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 1575-1595. doi: 10.3934/dcds.2012.32.1575

[15]

Claire david@lmm.jussieu.fr David, Pierre Sagaut. Theoretical optimization of finite difference schemes. Conference Publications, 2007, 2007 (Special) : 286-293. doi: 10.3934/proc.2007.2007.286

[16]

Elena Braverman, Alexandra Rodkina. Stochastic difference equations with the Allee effect. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 5929-5949. doi: 10.3934/dcds.2016060

[17]

Mehdi Pourbarat. On the arithmetic difference of middle Cantor sets. Discrete and Continuous Dynamical Systems, 2018, 38 (9) : 4259-4278. doi: 10.3934/dcds.2018186

[18]

Eugenia N. Petropoulou. On some difference equations with exponential nonlinearity. Discrete and Continuous Dynamical Systems - B, 2017, 22 (7) : 2587-2594. doi: 10.3934/dcdsb.2017098

[19]

Ali Akgül, Mustafa Inc, Esra Karatas. Reproducing kernel functions for difference equations. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : 1055-1064. doi: 10.3934/dcdss.2015.8.1055

[20]

Heide Gluesing-Luerssen, Fai-Lung Tsang. A matrix ring description for cyclic convolutional codes. Advances in Mathematics of Communications, 2008, 2 (1) : 55-81. doi: 10.3934/amc.2008.2.55

2021 Impact Factor: 1.015

Metrics

  • PDF downloads (216)
  • HTML views (152)
  • Cited by (0)

Other articles
by authors

[Back to Top]