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3-Colored 5-Designs and Z_4-Codes

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.

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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
Record Number:CaltechAUTHORS:20170927-153153707
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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, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81888
Deposited By: Tony Diaz
Deposited On:27 Sep 2017 22:41
Last Modified:15 Nov 2021 19:46

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