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(2010)DESIGNS CODES AND CRYPTOGRAPHY.56(2-3).p.219-233 Mark abstract This article studies the small weight codewords of the functional code C (Herm) (X), with X a non-singular Hermitian variety of PG(N, q (2)). The main result of this article is that the small weight codewords correspond to the intersections of X with the singular Hermitian varieties of PG(N, q (2)) consisting of q + 1 hyperplanes through a common (N - 2)-dimensional space I , forming a Baer subline in the quotient space of I . The number of codewords having these small weights is also calculated. In this way, similar results are obtained to the functional codes C (2)(Q), Q a non-singular quadric (Edoukou et al., J. Pure Appl. Algebra 214:1729-1739, 2010), and C (2)(X), X a non-singular Hermitian variety (Hallez and Storme, Finite Fields Appl. 16:27-35, 2010).

Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-1153804



Autor: Frederic AB Edoukou, Anja Hallez , Francois Rodier and Leo Storme

Fuente: https://biblio.ugent.be/publication/1153804



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