{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T13:01:55Z","timestamp":1772283715828,"version":"3.50.1"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[1993,7,1]],"date-time":"1993-07-01T00:00:00Z","timestamp":741484800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Des Codes Crypt"],"published-print":{"date-parts":[[1993,7]]},"DOI":"10.1007\/bf01388486","type":"journal-article","created":{"date-parts":[[2005,4,2]],"date-time":"2005-04-02T09:22:20Z","timestamp":1112433740000},"page":"251-275","source":"Crossref","is-referenced-by-count":15,"title":["Bounds for binary multiple covering codes"],"prefix":"10.1007","volume":"3","author":[{"given":"Heikki O.","family":"H\ufffdm\ufffdl\ufffdinen","sequence":"first","affiliation":[]},{"given":"Iiro S.","family":"Honkala","sequence":"additional","affiliation":[]},{"given":"Markku K.","family":"Kaikkonen","sequence":"additional","affiliation":[]},{"given":"Simon N.","family":"Litsyn","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/0097-3165(84)90010-4","volume":"36","author":"A. Blokhuis","year":"1984","unstructured":"Blokhuis, A. and Lam, C.W.H. 1984. More coverings by rook domains.J. Comb. Theory A. 36: 240?244.","journal-title":"J. Comb. Theory A."},{"key":"CR2","unstructured":"Chen, W. and Li, D. (forthcoming). Lower bounds for multiple covering codes."},{"key":"CR3","unstructured":"Clayton, R.F. 1987. Multiple packings and coverings in algebraic coding theory. Ph.D. Thesis, Univ. of California, Los Angeles."},{"key":"CR4","series-title":"Proc. AAECC-5. Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/3-540-51082-6_80","volume-title":"Nonlinear covering codes: A few results and conjectures","author":"G.D. Cohen","year":"1989","unstructured":"Cohen, G.D. 1989. Nonlinear covering codes: A few results and conjectures.Proc. AAECC-5. Lecture Notes in Computer Science 386, New York: Springer. pp. 225?229."},{"key":"CR5","unstructured":"Cohen, G.D., Honkala, I.S. and Litsyn, S.N. (forthcoming). On weighted coverings and packings with diameter one,Proc. Eurocode 92."},{"key":"CR6","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1109\/TIT.1985.1057043","volume":"31","author":"G.D. Cohen","year":"1985","unstructured":"Cohen, G.D., Karpovsky, M.R., Mattson, H.F. Jr. and Schatz, J.R. 1985. Covering radius-Survey and recent results.IEEE Trans. Inform. Theory. 31: 328?343.","journal-title":"IEEE Trans. Inform. Theory."},{"key":"CR7","unstructured":"Cohen, G.D., Litsyn, S.N. and Mattson, H.F. Jr. (forthcoming). Binary perfect weighted coverings.Sequences '91, Positano, 17?22 June 1991.Springer-Verlag Lecture Notes in Computer Science, Berlin, New York: Springer."},{"key":"CR8","doi-asserted-by":"crossref","unstructured":"Cohen, G.D., Litsyn, S.N. and Mattson, H.F. Jr. 1992. On perfect weighted coverings with small radius. First French-Soviet Workshop in Algebraic Coding, Paris, 22?24 July 1991,Springer-Verlag Lecture Notes in Computer Science 573, Berlin, New York, Heidelberg. 32?41.","DOI":"10.1007\/BFb0034338"},{"key":"CR9","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1109\/TIT.1986.1057227","volume":"32","author":"G.D. Cohen","year":"1986","unstructured":"Cohen, G.D., Lobstein, A.C. and Sloane, N.J.A. 1986. Further results on the covering radius of codes,IEEE Trans. Inform. Theory. 32: 680?694.","journal-title":"IEEE Trans. Inform. Theory."},{"key":"CR10","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1109\/TIT.1985.1057039","volume":"31","author":"R.L. Graham","year":"1985","unstructured":"Graham, R.L. and Sloane, N.J.A. 1985. On the covering radius of codes.IEEE Trans. Inform. Theory. 31: 385?401.","journal-title":"IEEE Trans. Inform. Theory."},{"key":"CR11","unstructured":"H\ufffdm\ufffdl\ufffdinen, H.O., Honkala, I.S. and Litsyn, S.N. (forthcoming). Bounds for binary codes that are multiple coverings of the farthest-off points."},{"key":"CR12","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/0097-3165(91)90024-B","volume":"56","author":"H. H\ufffdm\ufffdl\ufffdinen","year":"1991","unstructured":"H\ufffdm\ufffdl\ufffdinen, H. and Rankinen, S. 1991. Upper bounds for football pool problems and mixed covering codes.J. Comb. Theory A. 56: 84?95.","journal-title":"J. Comb. Theory A."},{"key":"CR13","unstructured":"Honkala, I.S. 1987. On the intersections and unions of Hamming spheres. In:The Very Knowledge of Coding, published on the occasion of the fiftieth birthday of Professor Aimo Tiet\ufffdv\ufffdinen, pp. 70?81, Turku."},{"key":"CR14","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1109\/18.2644","volume":"34","author":"I.S. Honkala","year":"1988","unstructured":"Honkala, I.S. 1988. Lower bounds for covering codes.IEEE Trans. Inform. Theory. 34: 326?329.","journal-title":"IEEE Trans. Inform. Theory."},{"key":"CR15","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1109\/18.75253","volume":"37","author":"I.S. Honkala","year":"1991","unstructured":"Honkala, I.S. 1991a. Modified bounds for covering codes.IEEE Trans. Inform. Theory. 37: 351?365.","journal-title":"IEEE Trans. Inform. Theory."},{"key":"CR16","doi-asserted-by":"crossref","first-page":"1203","DOI":"10.1109\/18.86975","volume":"37","author":"I.S. Honkala","year":"1991","unstructured":"Honkala, I.S. 1991b. On (k, t)-subnormal covering codes.IEEE Trans. Inform. Theory. 37: 1203?1206.","journal-title":"IEEE Trans. Inform. Theory."},{"key":"CR17","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/0012-365X(91)90028-Z","volume":"94","author":"I.S. Honkala","year":"1991","unstructured":"Honkala, I.S. 1991c. All binary codes with covering radius one are subnormal.Discrete Math. 94: 229?232.","journal-title":"Discrete Math."},{"key":"CR18","unstructured":"Honkala, I.S. (forthcoming a). On (q, 1)-subnormal q-ary covering codes.Discrete Appl. Math."},{"key":"CR19","unstructured":"Honkala, I.S. (forthcoming b). On the normality of multiple covering codes.Discrete Math."},{"key":"CR20","doi-asserted-by":"crossref","first-page":"1343","DOI":"10.1109\/18.21265","volume":"34","author":"I.S. Honkala","year":"1988","unstructured":"Honkala, I.S. and H\ufffdm\ufffdl\ufffdinen, H.O. 1988. A new construction for covering codes.IEEE Trans. Inform. Theory. 34: 1343?1344.","journal-title":"IEEE Trans. Inform. Theory."},{"key":"CR21","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1109\/18.75256","volume":"37","author":"I.S. Honkala","year":"1991","unstructured":"Honkala, I.S. and H\ufffdm\ufffdl\ufffdinen, H.O. 1991. Bounds for abnormal binary codes with covering radius one.IEEE Trans. Inform. Theory. 37: 372?375.","journal-title":"IEEE Trans. Inform. Theory."},{"key":"CR22","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1109\/18.54891","volume":"36","author":"X. Hou","year":"1990","unstructured":"Hou, X. 1990a. Some results on the norm of codes.IEEE Trans. Inform. Theory. 36: 683?685.","journal-title":"IEEE Trans. Inform. Theory."},{"key":"CR23","doi-asserted-by":"crossref","first-page":"1476","DOI":"10.1109\/18.59951","volume":"36","author":"X. Hou","year":"1990","unstructured":"Hou, X. 1990b. An improved sphere covering bound for the codes with n=3R+2.IEEE Trans. Inform. Theory. 36: 1476?1478.","journal-title":"IEEE Trans. Inform. Theory."},{"key":"CR24","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1109\/18.75258","volume":"37","author":"X. Hou","year":"1991","unstructured":"Hou, X. 1991. Binary linear quasi-perfect codes are normal.IEEE Trans. Inform. Theory. 37: 378?379.","journal-title":"IEEE Trans. Inform. Theory."},{"key":"CR25","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1016\/0097-3165(89)90036-8","volume":"52","author":"P.J.M. Laarhoven van","year":"1989","unstructured":"van Laarhoven, P.J.M., Aarts, E.H.L., van Lint, J.H. and Wille, L.T. 1989. New upper bounds for the football pool problem for 6, 7 and 8 matches.J. Combin. Theory Ser. A. 52: 304?312.","journal-title":"J. Combin. Theory Ser. A."},{"key":"CR26","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1137\/0608049","volume":"8","author":"K.E. Kilby","year":"1987","unstructured":"Kilby, K.E. and Sloane, N.J.A. 1987a. On the covering radius problem for codes I. Bounds on normalized covering radius.SIAM J. Algebraic Discrete Methods. 8: 604?618.","journal-title":"SIAM J. Algebraic Discrete Methods."},{"key":"CR27","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1137\/0608050","volume":"8","author":"K.E. Kilby","year":"1987","unstructured":"Kilby, K.E. and Sloane, N.J.A. 1987b. On the covering radius problem for codes II. Codes of low dimension; normal and abnormal codes.SIAM J. Algebraic and Discrete Methods. 8: 619?627.","journal-title":"SIAM J. Algebraic and Discrete Methods."},{"key":"CR28","unstructured":"Knapecz, G. 1989. Personal communication."},{"key":"CR29","unstructured":"Li, D. and Chen, W. (forthcoming). New lower bounds for binary covering codes."},{"key":"CR30","first-page":"7","volume-title":"Applied Algebra, Algebraic algorithms and Error-Correcting Codes: Proceedings of the 6th International Conference AAECC-6, Rome, Italy, July 1988","author":"J.H. Lint van","year":"1989","unstructured":"van Lint, J.H. 1989. Recent results on covering problems. InApplied Algebra, Algebraic algorithms and Error-Correcting Codes: Proceedings of the 6th International Conference AAECC-6, Rome, Italy, July 1988 (T. Mora, Ed.), Berlin: Springer-Verlag, pp. 7?21."},{"key":"CR31","unstructured":"van Lint, Jr., J.H. 1988. Covering radius problems. Master's Thesis, Eindhoven University of Technology."},{"key":"CR32","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1109\/18.45285","volume":"35","author":"A.C. Lobstein","year":"1989","unstructured":"Lobstein, A.C. and van Wee, G.J.M. 1989. On normal and subnormal q-ary codes.IEEE Trans. Inform. Theory. 35: 1291?1295 and 36: 1498.","journal-title":"IEEE Trans. Inform. Theory."},{"key":"CR33","volume-title":"The Theory of Error-Correcting Codes","author":"F.J. MacWilliams","year":"1977","unstructured":"MacWilliams, F.J. and Sloane, N.J.A. 1977.The Theory of Error-Correcting Codes. Amsterdam: North-Holland."},{"key":"CR34","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1109\/18.79926","volume":"37","author":"P.R.J. \ufffdsterg\ufffdrd","year":"1991","unstructured":"\ufffdsterg\ufffdrd, P.R.J. 1991a. Upper bounds forq-ary covering codes,IEEE Trans. Inform. Theory. 37: 660?664 and 1738.","journal-title":"IEEE Trans. Inform. Theory."},{"key":"CR35","unstructured":"\ufffdsterg\ufffdrd, P.R.J. 1991b. Construction of mixed covering codes, Report A 18, Digital Systems Laboratory, Helsinki Univ. of Technology."},{"key":"CR36","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1109\/18.108275","volume":"38","author":"P.R.J. \ufffdsterg\ufffdrd","year":"1992","unstructured":"\ufffdsterg\ufffdrd, P.R.J. 1992. Further results on (k, t)-subnormal covering codes.IEEE Trans. Inform. Theory. 38: 206?210.","journal-title":"IEEE Trans. Inform. Theory."},{"key":"CR37","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/0097-3165(86)90007-5","volume":"42","author":"N.J.A. Sloane","year":"1986","unstructured":"Sloane, N.J.A. 1986. A new approach to the covering radius of codes.J. Comb. Theory A. 42: 61?86.","journal-title":"J. Comb. Theory A."},{"key":"CR38","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1109\/18.2632","volume":"34","author":"G.J.M. Wee van","year":"1988","unstructured":"van Wee, G.J.M. 1988. Improved sphere bounds on the covering radius of codes.IEEE Trans. Inform. Theory. 34: 237?245.","journal-title":"IEEE Trans. Inform. Theory."},{"key":"CR39","doi-asserted-by":"crossref","first-page":"1466","DOI":"10.1109\/18.59947","volume":"36","author":"G.J.M. Wee van","year":"1990","unstructured":"van Wee, G.J.M. 1990. More binary covering codes are normal,IEEE Trans. Inform. Theory. 36: 1466?1470.","journal-title":"IEEE Trans. Inform. Theory."},{"key":"CR40","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1109\/18.79931","volume":"37","author":"G.J.M. Wee van","year":"1991","unstructured":"van Wee, G.J.M., Cohen, G.D. and Litsyn, S.N. 1991. A note on perfect multiple coverings of the Hamming space.IEEE Trans. Inform. Theory. 37: 678?682.","journal-title":"IEEE Trans. Inform. Theory."},{"key":"CR41","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/0097-3165(83)90032-8","volume":"35","author":"L.T. Wille","year":"1983","unstructured":"Wille, L.T. 1983. The football pool problem for 6 matches: A new upper bound.J. Comb. Theory A. 35: 106?108.","journal-title":"J. Comb. Theory A."},{"key":"CR42","unstructured":"Wille, L.T. Personal communication to G.D. Cohen."},{"key":"CR43","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1109\/18.79914","volume":"37","author":"Z. Zhang","year":"1991","unstructured":"Zhang, Z. 1991. Linear inequalities for covering codes: Part I?Pair covering inequalities.IEEE Trans. Inform. Theory. 37: 573?582.","journal-title":"IEEE Trans. Inform. Theory."},{"key":"CR44","doi-asserted-by":"crossref","first-page":"1648","DOI":"10.1109\/18.165440","volume":"38","author":"Z. Zhang","year":"1992","unstructured":"Zhang, Z. and Lo, C. 1992. Linear inequalities for covering codes: Part II?Triple convering inequalities.IEEE Trans. Inform. Theory. 38: 1648?1662.","journal-title":"IEEE Trans. Inform. Theory."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01388486\/fulltext.html","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01388486.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01388486\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01388486","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T16:14:19Z","timestamp":1556813659000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01388486"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,7]]},"references-count":44,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1993,7]]}},"alternative-id":["BF01388486"],"URL":"https:\/\/doi.org\/10.1007\/bf01388486","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,7]]}}}