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 Π, forming a Baer subline in the quotient space of Π. 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).
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Communicated by J. D. Key.
Dedicated to the memory of András Gács (1969–2009).
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Edoukou, F.A.B., Hallez, A., Rodier, F. et al. The small weight codewords of the functional codes associated to non-singular Hermitian varieties. Des. Codes Cryptogr. 56, 219–233 (2010). https://doi.org/10.1007/s10623-010-9401-0
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DOI: https://doi.org/10.1007/s10623-010-9401-0