{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T21:23:13Z","timestamp":1649107393441},"reference-count":20,"publisher":"Institute of Electronics, Information and Communications Engineers (IEICE)","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEICE Trans. Fundamentals"],"published-print":{"date-parts":[[2020,11,1]]},"DOI":"10.1587\/transfun.2020eal2003","type":"journal-article","created":{"date-parts":[[2020,5,13]],"date-time":"2020-05-13T22:07:39Z","timestamp":1589407659000},"page":"1292-1295","source":"Crossref","is-referenced-by-count":0,"title":["Asymptotically Optimal Codebooks in Regard to the Welch Bound with Characters"],"prefix":"10.1587","volume":"E103.A","author":[{"given":"Gang","family":"WANG","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Tianjin Normal University"}]},{"given":"Min-Yao","family":"NIU","sequence":"additional","affiliation":[{"name":"School of Sciences, Beijing University of Posts and Telecommunications"}]},{"given":"Lin-Zhi","family":"SHEN","sequence":"additional","affiliation":[{"name":"School of Sciences, Civil Aviation University of China"}]},{"given":"You","family":"GAO","sequence":"additional","affiliation":[{"name":"School of Sciences, Civil Aviation University of China"}]}],"member":"532","reference":[{"key":"1","doi-asserted-by":"publisher","unstructured":"[2] D.J. Love, R.W. Heath, and T. Strohmer, \u201cGrassmannian beamforming for multiple input multiple output wireless systems,\u201d IEEE Trans. Inf. Theory, vol.49, no.10, pp.2735-2747, Oct. 2003. 10.1109\/tit.2003.817466","DOI":"10.1109\/TIT.2003.817466"},{"key":"2","doi-asserted-by":"crossref","unstructured":"[3] L. Welch, \u201cLower bounds on the maximum cross correlation of signals,\u201d IEEE Trans. Inf. Theory, vol.20, no.3, pp.397-399, May 1974. 10.1109\/tit.1974.1055219","DOI":"10.1109\/TIT.1974.1055219"},{"key":"3","doi-asserted-by":"publisher","unstructured":"[4] B.M. Hochwald, T.L. Marzetta, T.J. Richardson, W. Sweldens, and R. Urbanke, \u201cSystematic design of unitary space-time constellations,\u201d IEEE Trans. Inf. Theory, vol.46, no.6, pp.1962-1973, Sept. 2000. 10.1109\/18.868472","DOI":"10.1109\/18.868472"},{"key":"4","doi-asserted-by":"publisher","unstructured":"[5] C. Ding and T. Feng, \u201cA generic construction of complex codebooks meeting the Welch bound,\u201d IEEE Trans. Inf. Theory, vol.53, no.11, pp.4245-4250, Nov. 2007. 10.1109\/tit.2007.907343","DOI":"10.1109\/TIT.2007.907343"},{"key":"5","doi-asserted-by":"publisher","unstructured":"[6] J. Conway, R. Harding, and N. Sloane, \u201cPacking lines, planes, etc.: Packings in Grassmannian spaces,\u201d Exp. Math., vol.5, no.2, pp.139-159, April 1996. 10.1080\/10586458.1996.10504585","DOI":"10.1080\/10586458.1996.10504585"},{"key":"6","doi-asserted-by":"publisher","unstructured":"[7] S. Li and G. Ge, \u201cDeterministic sensing matrices arising from near orthogonal systems,\u201d IEEE Trans. Inf. Theory, vol.60, no.4, pp.2291-2302, April 2014. 10.1109\/tit.2014.2303973","DOI":"10.1109\/TIT.2014.2303973"},{"key":"7","doi-asserted-by":"publisher","unstructured":"[8] P. Delsarte, J. Goethals, and J. Seidel, \u201cSpherical codes and designs,\u201d Geom. Dedicata, vol.6, no.3, pp.363-388, Sept. 1977. 10.1007\/bf03187604","DOI":"10.1007\/BF03187604"},{"key":"8","doi-asserted-by":"publisher","unstructured":"[10] P. Xia, S. Zhou, and G. Giannakis, \u201cAchieving the Welch bound with difference sets,\u201d IEEE Trans. Inf. Theory, vol.51, no.5, pp.1900-1907, May 2005. 10.1109\/tit.2005.846411","DOI":"10.1109\/TIT.2005.846411"},{"key":"9","doi-asserted-by":"publisher","unstructured":"[11] T. Strohmer and R. Heath, \u201cGrassmannian frames with applications to coding and communication,\u201d Appl. Comput. Harmon. Anal., vol.14, no.3, pp.257-275, May 2003. 10.1016\/s1063-5203(03)00023-x","DOI":"10.1016\/S1063-5203(03)00023-X"},{"key":"10","doi-asserted-by":"publisher","unstructured":"[12] C. Ding, \u201cComplex codebooks from combinatorial designs,\u201d IEEE Trans. Inf. Theory, vol.52, no.9, pp.4229-4235, Sept. 2006. 10.1109\/tit.2006.880058","DOI":"10.1109\/TIT.2006.880058"},{"key":"11","doi-asserted-by":"publisher","unstructured":"[13] M. Fickus, D. Mixon, and J. Tremain, \u201cSteiner equiangular tight frames,\u201d Linear Algebra Appl., vol.436, no.5, pp.1014-1027, March 2012. 10.1016\/j.laa.2011.06.027","DOI":"10.1016\/j.laa.2011.06.027"},{"key":"12","doi-asserted-by":"publisher","unstructured":"[14] M. Fickus, D. Mixon, and J. Jasper, \u201cEquiangular tight frames from hyperovals,\u201d IEEE Trans. Inf. Theory, vol.62, no.9, pp.5225-5236, Sept. 2016. 10.1109\/tit.2016.2587865","DOI":"10.1109\/TIT.2016.2587865"},{"key":"13","doi-asserted-by":"publisher","unstructured":"[15] Z. Zhou and X. Tang, \u201cNew nearly optimal codebooks from relative difference sets,\u201d Adv. Math. Commun., vol.5, no.3, pp.521-527, Aug. 2011. 10.3934\/amc.2011.5.521","DOI":"10.3934\/amc.2011.5.521"},{"key":"14","doi-asserted-by":"publisher","unstructured":"[16] C. Li, Q. Yue, and Y. Huang, \u201cTwo families of nearly optimal codebooks,\u201d Des. Codes Cryptogr., vol.75, no.1, pp.43-57, April 2015. 10.1007\/s10623-013-9891-7","DOI":"10.1007\/s10623-013-9891-7"},{"key":"15","doi-asserted-by":"publisher","unstructured":"[17] Z. Heng, C. Ding, and Q. Yue, \u201cNew constructions of asymptotically optimal codebooks with multiplicative characters,\u201d IEEE Trans. Inf. Theory, vol.63, no.10, pp.6179-6187, Oct. 2017. 10.1109\/tit.2017.2693204","DOI":"10.1109\/TIT.2017.2693204"},{"key":"16","doi-asserted-by":"publisher","unstructured":"[18] G. Luo and X. Cao, \u201cTwo constructions of asymptotically optimal codebooks via the hyper Eisenstein sum,\u201d IEEE Trans. Inf. Theory, vol.64, no.10, pp.6498-6505, Oct. 2017. 10.1109\/tit.2017.2777492","DOI":"10.1109\/TIT.2017.2777492"},{"key":"17","doi-asserted-by":"publisher","unstructured":"[19] L. Tian, Y. Li, T. Liu, and C. Xu, \u201cConstructions of codebooks asymptotically achieving the Welch bound with additive characters,\u201d IEEE Signal Process. Lett., vol.26, no.4, pp.622-626, April 2019. 10.1109\/lsp.2019.2891896","DOI":"10.1109\/LSP.2019.2891896"},{"key":"18","unstructured":"[20] R. Lidl and H. Niederreiter, Finite Fields, Cambridge Univ. Press, Cambridge, U.K., 1984."},{"key":"19","doi-asserted-by":"publisher","unstructured":"[21] S. Hong, H. Park, T. Helleseth, and Y. Kim, \u201cNear optimal partial Hadamard codebook construction using binary sequences obtained from quadratic residue mapping,\u201d IEEE Trans. Inf. Theory, vol.60, no.6, pp.3698-3705, June 2014. 10.1109\/tit.2014.2314298","DOI":"10.1109\/TIT.2014.2314298"},{"key":"20","doi-asserted-by":"publisher","unstructured":"[22] A. Zhang and K. Feng, \u201cTwo classes of codebooks nearly meeting the Welch bound,\u201d IEEE Trans. Inf. Theory, vol.58, no.4, pp.2507-2511, April 2012. 10.1109\/tit.2011.2176531","DOI":"10.1109\/TIT.2011.2176531"}],"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\/E103.A\/11\/E103.A_2020EAL2003\/_pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,7]],"date-time":"2020-11-07T03:31:22Z","timestamp":1604719882000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.jstage.jst.go.jp\/article\/transfun\/E103.A\/11\/E103.A_2020EAL2003\/_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,1]]},"references-count":20,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2020]]}},"URL":"https:\/\/doi.org\/10.1587\/transfun.2020eal2003","relation":{},"ISSN":["0916-8508","1745-1337"],"issn-type":[{"value":"0916-8508","type":"print"},{"value":"1745-1337","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,1]]}}}