Please use this identifier to cite or link to this item: http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/9430
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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