Bonnecaze, A. and Rains, E. and Solé, P. (2000) 3-Colored 5-Designs and Z_4-Codes. Journal of Statistical Planning and Inference, 86 (2). pp. 349-368. ISSN 0378-3758. doi:10.1016/S0378-3758(99)00117-2. https://resolver.caltech.edu/CaltechAUTHORS:20170927-153153707
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Abstract
New 5-designs on 24 points were constructed recently by Harada by the consideration of Z_4-codes. We use Jacobi polynomials as a theoretical tool to explain their existence as resulting of properties of the symmetrized weight enumerator (swe) of the code. We introduce the notion of a colored t-design and we show that the words of any given Lee composition, in any of the 13 Lee-optimal self-dual codes of length 24 over Z_4, form a colored 5-design. New colored 3-designs on 16 points are also constructed in that way.
| Item Type: | Article | |||||||||
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| Additional Information: | © 2000 Elsevier Science B.V. | |||||||||
| Subject Keywords: | Type II codes; Z_4-codes; Split weight enumerators; Jacobi polynomials; Invariant theory; Colored designs | |||||||||
| Issue or Number: | 2 | |||||||||
| DOI: | 10.1016/S0378-3758(99)00117-2 | |||||||||
| Record Number: | CaltechAUTHORS:20170927-153153707 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170927-153153707 | |||||||||
| Official Citation: | A. Bonnecaze, E. Rains, P. Solé, 3-Colored 5-Designs and Z4-Codes, In Journal of Statistical Planning and Inference, Volume 86, Issue 2, 2000, Pages 349-368, ISSN 0378-3758, https://doi.org/10.1016/S0378-3758(99)00117-2. (http://www.sciencedirect.com/science/article/pii/S0378375899001172) | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 81888 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 27 Sep 2017 22:41 | |||||||||
| Last Modified: | 15 Nov 2021 19:46 |
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