{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T08:23:39Z","timestamp":1750753419827},"reference-count":37,"publisher":"Institute of Electronics, Information and Communications Engineers (IEICE)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEICE Trans. Fundamentals"],"published-print":{"date-parts":[[2023,4,1]]},"DOI":"10.1587\/transfun.2022eap1037","type":"journal-article","created":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T22:15:42Z","timestamp":1664489742000},"page":"683-688","source":"Crossref","is-referenced-by-count":1,"title":["On the Construction of Variable Strength Orthogonal Arrays"],"prefix":"10.1587","volume":"E106.A","author":[{"given":"Qingjuan","family":"ZHANG","sequence":"first","affiliation":[{"name":"School of Economics and Statistics, Guangzhou University"}]},{"given":"Shanqi","family":"PANG","sequence":"additional","affiliation":[{"name":"College of Mathematics and Information Science, Henan Normal University"}]},{"given":"Yuan","family":"LI","sequence":"additional","affiliation":[{"name":"School of Economics and Statistics, Guangzhou University"}]}],"member":"532","reference":[{"key":"1","doi-asserted-by":"publisher","unstructured":"[1] J. Du, S.J. Fu, L.J. Qu, C. Li, and S.Q. Pang, \u201cNew constructions of q-variable 1-resilient rotation symmetric functions over &#120125;<i><sub>p<\/sub><\/i>,\u201d Sci. China Inf. Sci., vol.59, no.7, pp.1-3, 2016. 10.1007\/s11432-016-5569-x","DOI":"10.1007\/s11432-016-5569-x"},{"key":"2","doi-asserted-by":"publisher","unstructured":"[2] S.Q. Pang, X.N. Wang, J. Wang, J. Du, and M. Feng, \u201cConstruction and count of 1-resilient rotation symmetric Boolean functions,\u201d Inf. Sci., vol.450, pp.336-342, 2018. 10.1016\/j.ins.2018.03.052","DOI":"10.1016\/j.ins.2018.03.052"},{"key":"3","doi-asserted-by":"publisher","unstructured":"[3] S.Q. Pang, X. Zhang, X. Lin, and Q.J. Zhang \u201cTwo and three-uniform states from irredundant orthogonal arrays,\u201d NPJ Quantum Inf., vol.5, pp.1-10, 2019. 10.1038\/s41534-019-0165-8","DOI":"10.1038\/s41534-019-0165-8"},{"key":"4","doi-asserted-by":"publisher","unstructured":"[4] D. Goyeneche and K. Zyczkowski, \u201cGenuinely multipartite entangled states and orthogonal arrays,\u201d Phys. Rev. A, vol.90, 022316, 2014. 10.1103\/physreva.90.022316","DOI":"10.1103\/PhysRevA.90.022316"},{"key":"5","doi-asserted-by":"publisher","unstructured":"[5] D. Goyeneche, Z. Raissi, S.D. Martino, and K. Zyczkowski, \u201cEntanglement and quantum combinatorial designs,\u201d Phys. Rev. A, vol.97, 062326, 2018. 10.1103\/physreva.97.062326","DOI":"10.1103\/PhysRevA.97.062326"},{"key":"6","doi-asserted-by":"publisher","unstructured":"[6] J.W. Dong, D.Y. Pei, and X.L. Wang, \u201cA class of key predistribution schemes based on orthogonal arrays,\u201d J. Comput. Sci. Technol., vol.23, pp.825-831, 2008. 10.1007\/s11390-008-9168-1","DOI":"10.1007\/s11390-008-9168-1"},{"key":"7","doi-asserted-by":"publisher","unstructured":"[7] R. Mandl, \u201cOrthogonal latin squares: An application of experiment design to compiler testing,\u201d Commun. ACM, vol.28, no.10, pp.1054-1058, 1985. 10.1145\/4372.4375","DOI":"10.1145\/4372.4375"},{"key":"8","doi-asserted-by":"publisher","unstructured":"[8] R. Brownlie, J. Prowse, and M.S. Padke, \u201cRobust testing of AT&amp;T PMX\/StarMAIL using OATS,\u201d AT&amp;T Tech. J., vol.71, no.3, pp.41-47, 1992. 10.1002\/j.1538-7305.1992.tb00164.x","DOI":"10.1002\/j.1538-7305.1992.tb00164.x"},{"key":"9","doi-asserted-by":"publisher","unstructured":"[9] D.M. Cohen, S.R. Dalal, J. Parelius, and G.C. Patton, \u201cThe combinatorial design approach to automatic test generation,\u201d IEEE Softw., vol.13, no.5, pp.83-88, 1996. 10.1109\/52.536462","DOI":"10.1109\/52.536462"},{"key":"10","doi-asserted-by":"publisher","unstructured":"[10] D.M. Cohen, S.R. Dalal, M.L. Fredman, and G.C. Patton \u201cThe AETG system: An approach to testing based on combinatorial design,\u201d IEEE Trans. Softw., vol.23, no.7, pp.437-444, 1997. 10.1109\/32.605761","DOI":"10.1109\/32.605761"},{"key":"11","doi-asserted-by":"publisher","unstructured":"[11] L. Moura, J. Stardom, B. Stevens, and A. Williams, \u201cCovering arrays with mixed alphabet sizes,\u201d J. Combin. Designs, vol.11, no.6, pp.413-432, 2003. 10.1002\/jcd.10059","DOI":"10.1002\/jcd.10059"},{"key":"12","doi-asserted-by":"publisher","unstructured":"[12] C.J. Colbourn, S.S. Martirosyan, G.L. Mullen, D. Shasha, G.B. Sherwood, and J.L. Yucas, \u201cProducts of mixed covering arrays of strength two,\u201d J. Combin. Designs, vol.14, no.2, pp.124-138, 2006. 10.1002\/jcd.20065","DOI":"10.1002\/jcd.20065"},{"key":"13","doi-asserted-by":"publisher","unstructured":"[13] C.J. Colbourn, S.S. Martirosyan, T.V. Trung, and R.A. Walker, \u201cRoux-type constructions for covering arrays of strength three and four,\u201d Des. Codes, Cryptogr., vol.41, no.1, pp.33-57, 2006. 10.1007\/s10623-006-0020-8","DOI":"10.1007\/s10623-006-0020-8"},{"key":"14","doi-asserted-by":"publisher","unstructured":"[14] M.B. Cohen, C.J. Colbourn, and A.C.H. Ling, \u201cConstructing strength three covering arrays with augmented annealing,\u201d Discrete Math., vol.308, no.13, pp.2709-2722, 2008. 10.1016\/j.disc.2006.06.036","DOI":"10.1016\/j.disc.2006.06.036"},{"key":"15","doi-asserted-by":"publisher","unstructured":"[15] Y. Li, L.J. Ji, and J.X. Yin, \u201cCovering arrays of strength 3 and 4 from holey difference matrices,\u201d Des. Codes, Cryptogr., vol.50, no.3, pp.339-350, 2009. 10.1007\/s10623-008-9235-1","DOI":"10.1007\/s10623-008-9235-1"},{"key":"16","doi-asserted-by":"publisher","unstructured":"[16] L.J. Ji and J.X. Yin, \u201cConstructions of new orthogonal arrays and covering arrays of strength three,\u201d J. Comb. Theory, Ser. A, vol.117, no.3, pp.236-247, 2010. 10.1016\/j.jcta.2009.06.002","DOI":"10.1016\/j.jcta.2009.06.002"},{"key":"17","doi-asserted-by":"publisher","unstructured":"[17] C.J. Colbourn, C. Shi, C.M. Wang, and J. Yan, \u201cMixed covering arrays of strength three with few factors,\u201d J. Stat. Plan Inference, vol.141, no.11, pp.3640-3647, 2011. 10.1016\/j.jspi.2011.05.018","DOI":"10.1016\/j.jspi.2011.05.018"},{"key":"18","doi-asserted-by":"crossref","unstructured":"[18] M.B. Cohen, P.B. Gibbons, W.B. Mugridge, and C.J. Colbourn, \u201cConstructing test suites for interaction testing,\u201d Proc. 25th Intl. Conf. on Software Engineering, pp.38-48, May 2003. 10.1109\/icse.2003.1201186","DOI":"10.1109\/ICSE.2003.1201186"},{"key":"19","doi-asserted-by":"crossref","unstructured":"[19] M.B. Cohen, P.B. Gibbons, W.B. Mugridge, and C.J. Colbourn, \u201cVariable strength interaction testing of components,\u201d Proc. 27th Intel. Con. on Computer Software and Applications, pp.413-418, Nov. 2003. 10.1109\/cmpsac.2003.1245373","DOI":"10.1109\/CMPSAC.2003.1245373"},{"key":"20","doi-asserted-by":"crossref","unstructured":"[20] X. Chen, Q. Gu, A. Li, and D.X. Chen, \u201cVariable strength interaction testing with an ant colony system approach,\u201d Proc. 16th Asia-Pacific Software Engineering Conference, pp.160-167, 2009. 10.1109\/apsec.2009.18","DOI":"10.1109\/APSEC.2009.18"},{"key":"21","doi-asserted-by":"publisher","unstructured":"[21] S. Raaphorst, L. Moura, and B. Stevens, \u201cA construction for strength-3 covering arrays from linear feedback shift register sequences,\u201d Des. Codes, Cryptogr., vol.73, no.3, pp.949-968, 2013. 10.1007\/s10623-013-9835-2","DOI":"10.1007\/s10623-013-9835-2"},{"key":"22","doi-asserted-by":"publisher","unstructured":"[22] B.S. Ahmed, K.Z. Zamli, and C.P. Lim, \u201cApplication of particle swarm optimization to uniform and variable strength covering array construction,\u201d Appl. Soft Comput., vol.12, no.4, pp.1330-1347, 2012. 10.1016\/j.asoc.2011.11.029","DOI":"10.1016\/j.asoc.2011.11.029"},{"key":"23","doi-asserted-by":"publisher","unstructured":"[23] L. Jiang and J.X. Yin, \u201cAn approach of constructing mixed-level orthogonal arrays of strength\u22653,\u201d Sci. China Math., vol.56, no.6, pp.1109-1115, 2013. 10.1007\/s11425-013-4616-y","DOI":"10.1007\/s11425-013-4616-y"},{"key":"24","unstructured":"[24] C.Y. Suen, A. Das, and A. Dey, \u201cOn the construction of asymmetric orthogonal arrays,\u201d Stat. Sin., vol.11, pp.241-260, 2001."},{"key":"25","doi-asserted-by":"publisher","unstructured":"[25] Q.J. Zhang, Y. Li, S.Q. Pang, and X.F. Zhang, \u201cOn the construction of some new asymmetric orthogonal arrays,\u201d Commun. Stat. Theory Methods, https:\/\/doi.org\/10.1080\/03610926.2022.2083166, 2022. 10.1080\/03610926.2022.2083166","DOI":"10.1080\/03610926.2022.2083166"},{"key":"26","doi-asserted-by":"publisher","unstructured":"[26] C.Y. Suen and A. Dey, \u201cConstruction of asymmetric orthogonal arrays through finite geometries,\u201d J. Stat. Plan Inference, vol.115, pp.623-635, 2003. 10.1016\/s0378-3758(02)00165-9","DOI":"10.1016\/S0378-3758(02)00165-9"},{"key":"27","doi-asserted-by":"crossref","unstructured":"[27] A.S. Hedayat, N.J.A. Sloane, and J. Stufken, Orthogonal Arrays: Theory and Applications, Springer-Verlag, New York, 1999. 10.1007\/978-1-4612-1478-6","DOI":"10.1007\/978-1-4612-1478-6"},{"key":"28","doi-asserted-by":"publisher","unstructured":"[28] E.D. Schoen, P.T. Eendebak, and M.V.M. Nguyen, \u201cComplete enumeration of pure-level and mixed-level orthogonal arrays,\u201d J. Comb. Des., vol.18, no.2, pp.123-140, 2010. 10.1002\/jcd.20236","DOI":"10.1002\/jcd.20236"},{"key":"29","doi-asserted-by":"publisher","unstructured":"[29] S.Q. Pang, J. Wang, D.K.J. Lin, and M.Q. Liu, \u201cConstruction of mixed orthogonal arrays with high strength,\u201d Ann. Stat., vol.49, no.5, pp.2870-2884, 2021. 10.1214\/21-AOS2063","DOI":"10.1214\/21-AOS2063"},{"key":"30","doi-asserted-by":"publisher","unstructured":"[30] J. Wang, R.X. Yue, and S.Q. Pang, \u201cConstruction of asymmetric orthogonal arrays of high strength by juxtaposition,\u201d Commun. Stat. Theory Methods, vol.50, no.12, pp.2947-2957, 2019. 10.1080\/03610926.2019.1679184","DOI":"10.1080\/03610926.2019.1679184"},{"key":"31","doi-asserted-by":"publisher","unstructured":"[31] S.Q. Pang, X. Zhang, S.M. Fei, and Z.J. Zheng, \u201cQuantum k-uniform states for heterogeneous systems from irredundant mixed orthogonal arrays,\u201d Quantum Inf. Process., vol.20, https:\/\/doi.org\/10.1007\/s11128-021-03040-0, 2021. 10.1007\/s11128-021-03040-0","DOI":"10.1007\/s11128-021-03040-0"},{"key":"32","doi-asserted-by":"publisher","unstructured":"[32] S.Q. Pang, H.X. Xu, and M.Q. Chen, \u201cConstruction of binary quantum error-correcting codes from orthogonal array,\u201d Entropy, vol.24, no.7, https:\/\/doi.org\/10.3390\/e24071000, 2022. 10.3390\/e24071000","DOI":"10.3390\/e24071000"},{"key":"33","doi-asserted-by":"publisher","unstructured":"[33] X. Zhang, S.Q. Pang, and G.Z. Chen, \u201cConstruction of orthogonal arrays of strength three by augmented difference schemes,\u201d Discrete Math., vol.345, no.11, https:\/\/doi.org\/10.1016\/j.disc.2022.113041, 2022. 10.1016\/j.disc.2022.113041","DOI":"10.1016\/j.disc.2022.113041"},{"key":"34","doi-asserted-by":"publisher","unstructured":"[34] S.Q. Pang, X.K. Peng, X. Zhang, R.N. Zhang, and C.J. Yin, \u201c<i>k<\/i>-uniform states and quantum combinatorial designs,\u201d IEICE Trans. Fundamentals, vol.E105-A, no.6, pp.975-982, June 2022. 10.1587\/transfun.2021eap1090","DOI":"10.1587\/transfun.2021EAP1090"},{"key":"35","doi-asserted-by":"publisher","unstructured":"[35] J. Du, Q.Y. Wen, J. Zhang, and X. Liao, \u201cNew construction of symmetric orthogonal arrays of strength <i>t<\/i>,\u201d IEICE Trans. Fundamentals, vol.E96-A, no.9, pp.1901-1904, Sept. 2013. 10.1587\/transfun.e96.a.1901","DOI":"10.1587\/transfun.E96.A.1901"},{"key":"36","doi-asserted-by":"publisher","unstructured":"[36] S.Q. Pang, X. Lin, J. Du, and J. Wang, \u201cConstructions of asymmetric orthogonal arrays of strength <i>t<\/i> from orthogonal partitions of small orthogonal arrays,\u201d IEICE Trans. Fundamentals, vol.E101-A, no.8, pp.1267-1272, Aug. 2018. 10.1587\/transfun.e101.a.1267","DOI":"10.1587\/transfun.E101.A.1267"},{"key":"37","doi-asserted-by":"publisher","unstructured":"[37] S.Q. Pang, Y. Wang, J. Du, and W.J. Xu, \u201cIterative constructions of orthogonal arrays of strength <i>t<\/i> and orthogonal partitions,\u201d IEICE Trans. Fundamentals, vol.E100-A, no.1, pp.308-311, Jan. 2017. 10.1587\/transfun.e100.a.308","DOI":"10.1587\/transfun.E100.A.308"}],"container-title":["IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.jstage.jst.go.jp\/article\/transfun\/E106.A\/4\/E106.A_2022EAP1037\/_pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,4]],"date-time":"2024-10-04T23:35:46Z","timestamp":1728084946000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.jstage.jst.go.jp\/article\/transfun\/E106.A\/4\/E106.A_2022EAP1037\/_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,1]]},"references-count":37,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023]]}},"URL":"https:\/\/doi.org\/10.1587\/transfun.2022eap1037","relation":{},"ISSN":["0916-8508","1745-1337"],"issn-type":[{"type":"print","value":"0916-8508"},{"type":"electronic","value":"1745-1337"}],"subject":[],"published":{"date-parts":[[2023,4,1]]},"article-number":"2022EAP1037"}}