{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T08:04:48Z","timestamp":1761293088429},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2013,11,5]],"date-time":"2013-11-05T00:00:00Z","timestamp":1383609600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2015,4]]},"DOI":"10.1007\/s10623-013-9893-5","type":"journal-article","created":{"date-parts":[[2013,11,4]],"date-time":"2013-11-04T14:31:09Z","timestamp":1383575469000},"page":"81-95","source":"Crossref","is-referenced-by-count":21,"title":["Perfect codes in the discrete simplex"],"prefix":"10.1007","volume":"75","author":[{"given":"Mladen","family":"Kova\u010devi\u0107","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dejan","family":"Vukobratovi\u0107","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,11,5]]},"reference":[{"key":"9893_CR1","doi-asserted-by":"crossref","unstructured":"Aigner M.: Combinatorial Theory. Springer, New York (1979).","DOI":"10.1007\/978-1-4615-6666-3"},{"key":"9893_CR2","doi-asserted-by":"crossref","unstructured":"AlBdaiwi B., Horak P., Milazzo L.: Enumerating and decoding perfect linear Lee codes. Des. Codes Cryptogr. 52(2), 155\u2013162 (2009).","DOI":"10.1007\/s10623-009-9273-3"},{"key":"9893_CR3","unstructured":"Astola J.: On perfect Lee codes over small alphabets of odd cardinality. Discret. Appl. Math. 4, 227\u2013228 (1982)."},{"key":"9893_CR4","unstructured":"Bange D.W., Barkauskas A.E., Slater P.J.: Efficient dominating sets in graphs. In: Ringeisen R.D., Roberts F.S. (eds.) Applications of Discrete Mathematics, pp. 189\u2013199. SIAM, Philadelphia (1988)."},{"key":"9893_CR5","unstructured":"Bertsekas D.P., Gallager R.: Data Networks, 2nd edn. Prentice Hall, Englewood Cliffs (1992)."},{"key":"9893_CR6","unstructured":"Best M.R.: Perfect codes hardly exist. IEEE Trans. Inf. Theory 29(3), 349\u2013351 (1983)."},{"key":"9893_CR7","unstructured":"Biggs N.: Perfect codes in graphs. J. Comb. Theory B 15(3), 289\u2013296 (1973)."},{"key":"9893_CR8","doi-asserted-by":"crossref","unstructured":"Bours P.A.H.: On the construction of perfect deletion-correcting codes using design theory. Des. Codes Cryptogr. 6(1), 5\u201320 (1995).","DOI":"10.1007\/BF01390767"},{"key":"9893_CR9","unstructured":"Chihara L.: On the zeros of the Askey\u2013Wilson polynomials, with applications to coding theory. SIAM J. Math. Anal. 18(1), 191\u2013207 (1987)."},{"key":"9893_CR10","unstructured":"Cohen G., Honkala I., Litsyn S., Lobstein A.: Covering Codes. Elsevier, Amsterdam (1997)."},{"key":"9893_CR11","unstructured":"Delsarte P.: An algebraic approach to association schemes and coding theory. Philips J. Res. 10, 1\u201397 (1973)."},{"key":"9893_CR12","unstructured":"Etzion T.: On the nonexistence of perfect codes in the Johnson scheme. SIAM J. Discret. Math. 9(2), 201\u2013209 (1996)."},{"key":"9893_CR13","unstructured":"Etzion T.: Configuration distribution and designs of codes in the Johnson scheme. J. Comb. Des. 15(1), 15\u201334 (2007)."},{"key":"9893_CR14","unstructured":"Etzion T.: Product constructions for perfect Lee codes. IEEE Trans. Inf. Theory 57(11), 7473\u20137481 (2011)."},{"key":"9893_CR15","unstructured":"Etzion T., Schwartz M.: Perfect constant-weight codes. IEEE Trans. Inf. Theory 50(9), 2156\u20132165 (2004)."},{"key":"9893_CR16","unstructured":"Etzion T., Vardy A.: Perfect binary codes: constructions, properties, and enumeration. IEEE Trans. Inf. Theory 40(3), 754\u2013763 (1994)."},{"key":"9893_CR17","unstructured":"Etzion T., Vardy A.: Error-correcting codes in projective space. IEEE Trans. Inf. Theory 57(2), 1165\u20131173 (2011)."},{"key":"9893_CR18","unstructured":"Gadouleau M., Goupil A.: Binary codes for packet error and packet loss correction in store and forward. In: Proceedings of the International ITG Conference on Source and Channel Coding, Siegen, Germany (2010)"},{"key":"9893_CR19","unstructured":"Gadouleau M., Goupil A.: A matroid framework for noncoherent random network communications. IEEE Trans. Inf. Theory 57(2), 1031\u20131045 (2011)."},{"key":"9893_CR20","unstructured":"Golomb S.W., Welch L.R.: Perfect codes in the Lee metric and the packing of polyominoes. SIAM J. Appl. Math. 18(2), 302\u2013317 (1970)."},{"key":"9893_CR21","unstructured":"Gordon D.M.: Perfect single error-correcting codes in the Johnson scheme. IEEE Trans. Inf. Theory 52(10), 4670\u20134672 (2006)."},{"key":"9893_CR22","unstructured":"Horak P.: Tilings in Lee metric. Eur. J. Comb. 30(2), 480\u2013489 (2009)."},{"key":"9893_CR23","unstructured":"Horak P.: On perfect Lee codes. Discret. Math. 309(18), 5551\u20135561 (2009)."},{"key":"9893_CR24","unstructured":"K\u00f6tter R., Kschischang F.R.: Coding for errors and erasures in random network coding. IEEE Trans. Inf. Theory 54(8), 3579\u20133591 (2008)."},{"key":"9893_CR25","unstructured":"Kova\u010devi\u0107 M., Vukobratovi\u0107 D.: Subset codes for packet networks. IEEE Commun. Lett. 17(4), 729\u2013732 (2013)."},{"key":"9893_CR26","unstructured":"Kova\u010devi\u0107 M., Vukobratovi\u0107 D.: Multiset codes for permutation channels. Available online at: arXiv:1301.7564."},{"key":"9893_CR27","unstructured":"Levenshtein V.I.: On perfect codes in deletion and insertion metric. Discret. Math. Appl. 2(3), 241\u2013258 (1992)."},{"key":"9893_CR28","unstructured":"MacWilliams F.J., Sloane N.J.A.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1977)."},{"key":"9893_CR29","doi-asserted-by":"crossref","unstructured":"Martin W.J., Zhu X.J.: Anticodes for the Grassmann and bilinear forms graphs. Des. Codes Cryptogr. 6(1), 73\u201379 (1995).","DOI":"10.1007\/BF01390772"},{"key":"9893_CR30","doi-asserted-by":"crossref","unstructured":"Post K.A.: Nonexistence theorem on perfect Lee codes over large alphabets. Inf. Control 29(4), 369\u2013380 (1975).","DOI":"10.1016\/S0019-9958(75)80005-2"},{"key":"9893_CR31","unstructured":"Roos C.: A note on the existence of perfect constant weight codes. Discret. Math. 47, 121\u2013123 (1983)."},{"key":"9893_CR32","unstructured":"Shimabukuro O.: On the nonexistence of perfect codes in $$ J(2w + p2, w)$$ J ( 2 w + p 2 , w ) . Ars Comb. 75, 129\u2013134 (2005)."},{"key":"9893_CR33","unstructured":"\u0160pacapan S.: Non-existence of face-to-face four dimensional tiling in the Lee metric. Eur. J. Comb. 28(1), 127\u2013133 (2007)."},{"key":"9893_CR34","unstructured":"Tiet\u00e4v\u00e4inen A.: On the nonexistence of perfect codes over finite fields. SIAM J. Appl. Math. 24(1), 88\u201396 (1973)."},{"key":"9893_CR35","unstructured":"van Lint J. H.: Nonexistence theorems for perfect error-correcting codes. In: Computers in Algebra and Number Theory, vol. IV, SIAM-AMS Proceedings (1971)."},{"key":"9893_CR36","unstructured":"Zinoviev V.A., Leontiev V.K.: The nonexistence of perfect codes over Galois fields. Probl. Control Inf. Theory 2, 123\u2013132 (1973)."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-013-9893-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10623-013-9893-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-013-9893-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T19:58:37Z","timestamp":1559246317000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10623-013-9893-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,5]]},"references-count":36,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,4]]}},"alternative-id":["9893"],"URL":"https:\/\/doi.org\/10.1007\/s10623-013-9893-5","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,11,5]]}}}