Name
Title | ||
|---|---|---|
The small weight codewords of the functional codes associated to non-singular Hermitian varieties |
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 驴 2)-dimensional space 驴, forming a Baer subline in the quotient space of 驴. 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). |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1007/s10623-010-9401-0 | Des. Codes Cryptography |
Keywords | Field | DocType |
Functional codes,Hermitian variety,Small weight codewords,05B25,51A50,94B27 | Discrete mathematics,Finite field,Combinatorics,Quotient space (topology),Hyperplane,Hermitian matrix,Hermitian variety,Quadric,Mathematics | Journal |
Volume | Issue | ISSN |
56 | 2-3 | 0925-1022 |
Citations | PageRank | References |
9 | 1.27 | 3 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| frederic a b edoukou | 1 | 33 | 5.99 |
| Anja Hallez | 2 | 25 | 4.61 |
| François Rodier | 3 | 39 | 9.83 |
| L. Storme | 4 | 217 | 36.02 |