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Title: | Higher weight spectra of ternary codes associated to the quadratic Veronese 3-fold |
Authors: | KAIPA, KRISHNA PRADHAN, PUSPENDU Dept. of Mathematics |
Keywords: | Quadratic Veronese varieties Veronese code Linear system of quadrics Generalized weight enumerator polynomial Extended weight enumerator polynomial 2025-MAR-WEEK4 TOC-MAR-2025 2025 |
Issue Date: | Mar-2025 |
Publisher: | World Scientific Publishing Co. |
Citation: | Journal of Algebra and Its Applications |
Abstract: | The problem studied in this work is to determine the higher weight spectra of the Projective Reed–Muller codes associated to the Veronese 3 -fold V in P G ( 9 , q ) , which is the image of the quadratic Veronese embedding of P G ( 3 , q ) in P G ( 9 , q ) . We reduce the problem to the following combinatorial problem in finite geometry: For each subset S of V , determine the dimension of the linear subspace of P G ( 9 , q ) generated by S . We develop a systematic method to solve the latter problem. We implement the method for q = 3 , and use it to obtain the higher weight spectra of the associated code. The case of a general finite field F q will be treated in a future work. |
URI: | https://doi.org/10.1142/S0219498825410075 http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/9430 |
ISSN: | 0219-4988 1793-6829 |
Appears in Collections: | JOURNAL ARTICLES |
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