{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,26]],"date-time":"2024-08-26T07:10:45Z","timestamp":1724656245691},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2024,5,9]],"date-time":"2024-05-09T00:00:00Z","timestamp":1715212800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,5,9]],"date-time":"2024-05-09T00:00:00Z","timestamp":1715212800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cryptogr. Commun."],"published-print":{"date-parts":[[2024,9]]},"DOI":"10.1007\/s12095-024-00720-3","type":"journal-article","created":{"date-parts":[[2024,5,9]],"date-time":"2024-05-09T08:01:51Z","timestamp":1715241711000},"page":"1077-1102","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Additive codes with few weights"],"prefix":"10.1007","volume":"16","author":[{"given":"Daniel","family":"Panario","sequence":"first","affiliation":[]},{"given":"Murat","family":"Sahin","sequence":"additional","affiliation":[]},{"given":"Qiang","family":"Wang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,5,9]]},"reference":[{"key":"720_CR1","doi-asserted-by":"publisher","first-page":"2010","DOI":"10.1109\/18.705584","volume":"44","author":"A Ashikhmin","year":"1998","unstructured":"Ashikhmin, A., Barg, A.: Minimal vectors in linear codes. IEEE T. Inform. Theory 44, 2010\u20132017 (1998)","journal-title":"IEEE T. Inform. Theory"},{"key":"720_CR2","first-page":"225","volume":"12","author":"C Bachoc","year":"2000","unstructured":"Bachoc, C., Gaborit, P.: On extremal additive GF(4)-codes of lengths 10 to 18. J. Theorie Nombres Bordeaux 12, 225\u2013271 (2000)","journal-title":"J. Theorie Nombres Bordeaux"},{"key":"720_CR3","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/j.ffa.2015.06.005","volume":"36","author":"J Bierbrauer","year":"2015","unstructured":"Bierbrauer, J., Bartoli, D., Faina, G., Marcugini, S., Pambianco, F.: The nonexistence of an additive quaternary [15,5,9]-code. Finite Fields Their Appl. 36, 29\u201340 (2015)","journal-title":"Finite Fields Their Appl."},{"key":"720_CR4","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1109\/12.364531","volume":"44","author":"M Blaum","year":"1995","unstructured":"Blaum, M., Brady, J., Bruck, J., Menon, J.: EVENODD: An efficient scheme for tolerating double disk failures in RAID architectures. IEEE Trans. Comput. 44, 192\u2013202 (1995)","journal-title":"IEEE Trans. Comput."},{"key":"720_CR5","doi-asserted-by":"publisher","first-page":"906","DOI":"10.1109\/18.53756","volume":"36","author":"M Blaum","year":"1990","unstructured":"Blaum, M., Bruck, J.: Decoding the Golay code with Venn diagrams. IEEE Trans. Inf. Theory 36, 906\u2013910 (1990)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"720_CR6","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1109\/18.485722","volume":"42","author":"M Blaum","year":"1995","unstructured":"Blaum, M., Bruck, J., Vardy, A.: MDS array codes with independent parity symbols. IEEE Trans. Inf. Theory 42, 529\u2013542 (1995)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"2","key":"720_CR7","first-page":"1855","volume":"1","author":"M Blaum","year":"1998","unstructured":"Blaum, M., Farrell, P.G., van Tilborg, H.C.A.: Array codes in Handbook of Coding Theory. North-Holland, Amsterdam 1(2), 1855\u20131909 (1998)","journal-title":"North-Holland, Amsterdam"},{"key":"720_CR8","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1109\/18.179343","volume":"39","author":"M Blaum","year":"1993","unstructured":"Blaum, M., Roth, R.M.: New array codes for multiple phased burst correction. IEEE Trans. Inf. Theory 39, 66\u201377 (1993)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"720_CR9","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1109\/18.746771","volume":"45","author":"M Blaum","year":"1999","unstructured":"Blaum, M., Roth, R.M.: On lowest density MDS codes. IEEE Trans. Inf. Theory 45, 46\u201359 (1999)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"720_CR10","doi-asserted-by":"publisher","first-page":"1369","DOI":"10.1109\/18.681315","volume":"44","author":"AR Calderbank","year":"1998","unstructured":"Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction via codes over GF(4). IEEE Trans. Inf. Theory 44, 1369\u20131387 (1998)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"720_CR11","first-page":"47","volume":"45","author":"SD Cardell","year":"2013","unstructured":"Cardell, S.D., Climent, J.J., Requena, V.: A construction of MDS array codes. WIT Trans. Inf. Commun. Technol. 45, 47\u201358 (2013)","journal-title":"WIT Trans. Inf. Commun. Technol."},{"key":"720_CR12","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1023\/A:1008344232130","volume":"15","author":"C Carlet","year":"1998","unstructured":"Carlet, C., Charpin, P., Zinoviev, V.: Codes, bent functions and permutations suitable for DES-like cryptosystems. Des. Codes Cryptogr. 15, 125\u2013156 (1998)","journal-title":"Des. Codes Cryptogr."},{"key":"720_CR13","doi-asserted-by":"publisher","first-page":"2089","DOI":"10.1109\/TIT.2005.847722","volume":"51","author":"C Carlet","year":"2005","unstructured":"Carlet, C., Ding, C., Yuan, J.: Linear codes from perfect nonlinear mappings and their secret sharing schemes. IEEE Trans. Inf. Theory 51, 2089\u20132102 (2005)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"720_CR14","first-page":"171","volume":"28","author":"RS Coulter","year":"1999","unstructured":"Coulter, R.S.: On the evaluation of a class of Weil sums in characteristics 2. New Zealand J. Math. 28, 171\u2013184 (1999)","journal-title":"New Zealand J. Math."},{"key":"720_CR15","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/s10623-010-9469-6","volume":"59","author":"LE Danielsen","year":"2011","unstructured":"Danielsen, L.E., Parker, M.G.: Directed graph representation of half-rate additive codes over GF(4). Des. Codes Cryptogr. 59, 119\u2013130 (2011)","journal-title":"Des. Codes Cryptogr."},{"key":"720_CR16","doi-asserted-by":"publisher","first-page":"3265","DOI":"10.1109\/TIT.2015.2420118","volume":"61","author":"C Ding","year":"2015","unstructured":"Ding, C.: Linear codes from some 2-designs. IEEE Trans. Inf. Theory 61, 3265\u20133275 (2015)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"720_CR17","doi-asserted-by":"publisher","first-page":"2288","DOI":"10.1016\/j.disc.2016.03.029","volume":"339","author":"C Ding","year":"2016","unstructured":"Ding, C.: A construction of binary linear codes from Boolean functions. Discrete Math. 339, 2288\u20132323 (2016)","journal-title":"Discrete Math."},{"key":"720_CR18","doi-asserted-by":"publisher","first-page":"1879","DOI":"10.1109\/LCOMM.2014.2361516","volume":"18","author":"K Ding","year":"2014","unstructured":"Ding, K., Ding, C.: Binary linear codes with three weights. IEEE Commun. Lett. 18, 1879\u20131882 (2014)","journal-title":"IEEE Commun. Lett."},{"key":"720_CR19","doi-asserted-by":"publisher","first-page":"5835","DOI":"10.1109\/TIT.2015.2473861","volume":"61","author":"K Ding","year":"2015","unstructured":"Ding, K., Ding, C.: A class of two-weight and three-weight codes and their applications in secret sharing. IEEE Trans. Inf. Theory 61, 5835\u20135842 (2015)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"720_CR20","doi-asserted-by":"publisher","first-page":"2274","DOI":"10.1109\/TIT.2007.896886","volume":"53","author":"C Ding","year":"2007","unstructured":"Ding, C., Niederreiter, H.: Cyclotomic linear codes of order 3. IEEE Trans. Inf. Theory 53, 2274\u20132277 (2007)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"720_CR21","doi-asserted-by":"crossref","unstructured":"Ding, C., Yuan, J.: Covering and secret sharing with linear codes. In: International Conference on Discrete Mathematics and Theoretical Computer Science (DMTCS); Dijon, France. 11\u201325, (2003)","DOI":"10.1007\/3-540-45066-1_2"},{"key":"720_CR22","unstructured":"Gaborit, P., Huffman, W. C., Kim, J. L., Pless, V.: On the classification of extremal additive codes over GF(4). In Proceedings of the 37th Allerton Conference on Communication, Control, and Computing, Urbana-Champaign, 535\u2013544, (1999)"},{"key":"720_CR23","doi-asserted-by":"crossref","unstructured":"Gaborit, P., Huffman, W. C., Kim, J. L., Pless, V.: On additive GF(4) codes. DIMACS Workshop on Codes and Association Schemes, DIMACS Series in Discrete Math. and Theoret. Computer Science, Amer. Math. Soc., Providence, RI, vol. 56, 135\u2013149, (2001)","DOI":"10.1090\/dimacs\/056\/12"},{"key":"720_CR24","volume-title":"Redundant Disk Arrays: Reliable, Parallel Secondary Storage","author":"GA Gibson","year":"1992","unstructured":"Gibson, G.A.: Redundant Disk Arrays: Reliable, Parallel Secondary Storage. MIT Press, Cambridge, MA (1992)"},{"key":"720_CR25","doi-asserted-by":"publisher","first-page":"2832","DOI":"10.1016\/j.disc.2016.05.033","volume":"339","author":"Z Heng","year":"2016","unstructured":"Heng, Z., Yue, Q., Li, C.: Three classes of linear codes with two or three weights. Discrete Math. 339, 2832\u20132847 (2016)","journal-title":"Discrete Math."},{"key":"720_CR26","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1007\/s00208-003-0440-y","volume":"327","author":"G H\u00f6hn","year":"2003","unstructured":"H\u00f6hn, G.: Self-dual codes over the Kleinian four group. Math. Ann. 327, 227\u2013255 (2003)","journal-title":"Math. Ann."},{"key":"720_CR27","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1016\/j.ffa.2019.02.001","volume":"57","author":"G Jian","year":"2019","unstructured":"Jian, G., Lin, Z., Feng, R.: Two-weight and three-weight linear codes based on Weil sums. Finite Fields Appl. 57, 92\u2013107 (2019)","journal-title":"Finite Fields Appl."},{"key":"720_CR28","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/s00200-016-0296-5","volume":"28","author":"JL Kim","year":"2017","unstructured":"Kim, J.L., Lee, N.: Secret sharing schemes based on additive codes over GF(4). Appl. Algebra Engrg. Comm. Comput. 28, 79\u201397 (2017)","journal-title":"Appl. Algebra Engrg. Comm. Comput."},{"key":"720_CR29","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1007\/s00200-016-0297-4","volume":"28","author":"C Li","year":"2017","unstructured":"Li, C., Yue, Q., Fu, F.: A construction of several classes of two-weight and three-weight linear codes. Appl. Algebra Engrg. Comm. Comput. 28, 11\u201330 (2017)","journal-title":"Appl. Algebra Engrg. Comm. Comput."},{"key":"720_CR30","doi-asserted-by":"publisher","first-page":"195","DOI":"10.3934\/amc.2019013","volume":"13","author":"C Li","year":"2019","unstructured":"Li, C., Bae, S., Yang, S.: Some two-weight and three-weight linear codes. Adv. Math. Commun. 13, 195\u2013211 (2019)","journal-title":"Adv. Math. Commun."},{"key":"720_CR31","unstructured":"Lidl, R., Mullen, G.L., Turnwald, G.: Dickson Polynomials. Pitman Monographs Surv. Pure Appl. Math. 65, (1993)"},{"key":"720_CR32","doi-asserted-by":"publisher","first-page":"3186","DOI":"10.1109\/TIT.2006.876235","volume":"52","author":"E Louidor","year":"2006","unstructured":"Louidor, E., Roth, R.M.: Lowest density MDS codes over extension alphabets. IEEE Trans. Inf. Theory 52, 3186\u20133197 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"720_CR33","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1007\/s12095-020-00435-1","volume":"12","author":"N Li","year":"2020","unstructured":"Li, N., Mesnager, S.: Recent results and problems on constructions of linear codes from cryptographic functions. Cryptogr. Commun. 12, 965\u2013986 (2020)","journal-title":"Cryptogr. Commun."},{"key":"720_CR34","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/s12095-016-0186-5","volume":"9","author":"S Mesnager","year":"2017","unstructured":"Mesnager, S.: Linear codes with few weights from weakly regular bent functions based on a generic construction. Cryptogr. Commun. 9, 71\u201384 (2017)","journal-title":"Cryptogr. Commun."},{"key":"720_CR35","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1007\/s10623-018-0556-4","volume":"87","author":"S Mesnager","year":"2019","unstructured":"Mesnager, S., \u00d6zbudak, F., Sinak, A.: Linear codes from weakly regular plateaued functions and their secret sharing schemes. Des. Codes Cryptogr. 87, 463\u2013480 (2019)","journal-title":"Des. Codes Cryptogr."},{"key":"720_CR36","doi-asserted-by":"publisher","first-page":"1166","DOI":"10.1109\/TIT.2016.2518678","volume":"62","author":"C Tang","year":"2016","unstructured":"Tang, C., Li, N., Qi, Y., Zhou, Z., Helleseth, T.: Linear codes with two or three weights from weakly regular bent functions. IEEE Trans. Inf. Theory 62, 1166\u20131176 (2016)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"720_CR37","doi-asserted-by":"publisher","first-page":"3055","DOI":"10.1016\/j.disc.2017.07.008","volume":"340","author":"D Tang","year":"2017","unstructured":"Tang, D., Carlet, C., Zhou, Z.: Binary linear codes from vectorial boolean functions and their weight distribution. Discrete Math. 340, 3055\u20133072 (2017)","journal-title":"Discrete Math."},{"key":"720_CR38","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/BF01810572","volume":"2","author":"J Wolfmann","year":"1991","unstructured":"Wolfmann, J.: Polynomial description of binary linear codes and related properties. Appl. Algebra Engrg. Comm. Comput. 2, 119\u2013138 (1991)","journal-title":"Appl. Algebra Engrg. Comm. Comput."},{"key":"720_CR39","doi-asserted-by":"publisher","first-page":"1255","DOI":"10.1007\/s10623-020-00744-9","volume":"88","author":"Y Wu","year":"2020","unstructured":"Wu, Y., Li, N., Zeng, X.: Linear codes with few weights from cyclotomic classes and weakly regular bent functions. Des. Codes Cryptogr. 88, 1255\u20131272 (2020)","journal-title":"Des. Codes Cryptogr."},{"key":"720_CR40","unstructured":"Xiang, C.:It is indeed a fundamental construction of all linear codes. (2016) https:\/\/arxiv.org\/pdf\/1610.06355.pdf"},{"key":"720_CR41","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1109\/TIT.2016.2620497","volume":"63","author":"C Xiang","year":"2017","unstructured":"Xiang, C., Feng, K., Tang, C.: A Construction of linear codes over $$\\mathbb{F} _2$$ from Boolean functions. IEEE Trans. Inf. Theory 63, 169\u2013176 (2017)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"720_CR42","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1109\/18.746809","volume":"45","author":"LH Xu","year":"1999","unstructured":"Xu, L.H., Bruck, J.: X-code: MDS array codes with optimal encoding. IEEE Trans. Inf. Theory 45, 272\u2013276 (1999)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"720_CR43","doi-asserted-by":"publisher","first-page":"712","DOI":"10.1109\/TIT.2005.862125","volume":"52","author":"J Yuan","year":"2006","unstructured":"Yuan, J., Carlet, C., Ding, C.: The weight distributions of a class of linear codes from perfect nonlinear functions. IEEE Trans. Inf. Theory 52, 712\u2013716 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"720_CR44","first-page":"197","volume":"19","author":"GV Zaitzev","year":"1983","unstructured":"Zaitzev, G.V., Zinovev, V.A., Semakov, N.V.: Minimum-check-density codes for correcting bytes of errors, erasures, or defects. Probl. Inf. Transm. 19, 197\u2013204 (1983)","journal-title":"Probl. Inf. Transm."}],"container-title":["Cryptography and Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-024-00720-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12095-024-00720-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-024-00720-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,26]],"date-time":"2024-08-26T06:09:09Z","timestamp":1724652549000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12095-024-00720-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,9]]},"references-count":44,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["720"],"URL":"https:\/\/doi.org\/10.1007\/s12095-024-00720-3","relation":{},"ISSN":["1936-2447","1936-2455"],"issn-type":[{"type":"print","value":"1936-2447"},{"type":"electronic","value":"1936-2455"}],"subject":[],"published":{"date-parts":[[2024,5,9]]},"assertion":[{"value":"9 November 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 May 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 May 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}