2 edition of Quadrics, hermitian varieties, and bounds on error correcting codes found in the catalog.
Quadrics, hermitian varieties, and bounds on error correcting codes
R. C. Bose
by Research and Training School, Indian Statistical Institute in Calcutta
Written in English
|Statement||by R. C. Bose.|
|Series||Indian Statistical Institute. Research and Training School. Mimeographed ser., publication no. M 66-1|
|LC Classifications||QA167.2 .B67|
|The Physical Object|
|Pagination||iii, 144 p.|
|Number of Pages||144|
|LC Control Number||73900538|
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Index error: index is out of bounds for axis 0 with size Hot Network Questions Does this article claim that Australian citizens of Chinese . Many of these substructures are investigated for their geometrical importance, such as the quadrics and the Hermitian varieties, but many substructures are investigated because of their links to other research areas such as coding theory. This includes the link between arcs in Galois geometries and linear MDS codes.
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In recent years, functional codes have received much attention. In his PhD thesis, F.A.B. Edoukou investigated various functional codes linked to quadrics and Hermitian varieties defined in finite projective spaces (Edoukou, PhD Thesis, ). This work was continued in (Edoukou et al., Des Codes Cryptogr –, ; Edoukou et al., J Pure Appl Algebr Cited by: 9.
6 Franz Lemmermeyer Error-Correcting Codes If the remainder modulo 11 turns out to be 10, we will use X (the letter for 10 used by the Romans) to denote the.
On Quasi-Hermitian Varieties. error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the. This short note offers a contribution to the theory of error-correcting codes from higher-dimensional projective varieties along the lines of S.
Chakravarti I.M. () Families of Codes with Few Distinct Weights from Singular and Non-Singular Hermitian Varieties and Quadrics in Projective Geometries and Hadamard Difference Sets and Designs Associated with Two-Weight Codes.
In: Coding Theory and Design Theory. The IMA Volumes in Mathematics hermitian varieties Its Applications, vol Springer, New Cited by: Functional codes arising from quadric intersections with Quadrics varieties A.
Hallez L. Storme J Abstract We investigate the functional code C h(X) introduced by G. Lachaud  in the special case where X is a non-singular Hermitian variety in PG(N;q2) and h = 2. Families of codes with few distinct weights from singular and non-singular, Hermitian varieties and quadrics in projective geometries and Hadamard difference sets and designs associated with two-weight codes: Author: Chakravarti, I.
Publisher: North Carolina State University. Dept. of Statistics: Date: Series/Report No.:Cited by: We refer to, for codes defined on a Hermitian variety by quadratic forms and for the converse, i.e.
codes defined by Hermitian forms on a quadric. In both cases, it appears that the maximum cardinality should be attained when one of the varieties splits in the union of hyperplanes, even if this, in the case of , is, for the time Cited by: 3.
We study the functional codes of second order deﬁned by G. Lachaud on X ⊂ P4(F q) a quadric of rank(X)=3,4,5 or a non-degenerate hermitian variety. We give some bounds for the number of points of quadratic sections of X, which are the best possible and show that codes deﬁned on non-degenerate quadrics are better than those deﬁned on.
Algebraic Geometry Codes: Advanced Chapters is devoted to the theory of algebraic geometry codes, a subject related to several domains of mathematics. On one hand, it involves such classical areas as algebraic geometry and number theory; on the other, it is connected to information transmission theory, combinatorics, finite geometries, dense.
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Evaluating the following function gives the error: The quadrics are observed to be symmetric therefore only 10 numbers instead of 16 need to be stored. When an edge is collapsed, the quadrics should be unioned but as observed by , addition may add some imprecision but the benefits in terms of speed outweigh unioning the quadrics.
Full text of "Applied algebra, algebraic algorithms, and error-correcting codes: 13th international symposium, AAECC, Honolulu, Hawaii, USA, November 15. the cohomology of some special varieties, namely the complete intersection of two quadrics; this enables me to check directly that certain well known conjectures hold in the case of these varieties.
This introduction is devoted to a brief sketch of what is known, and what the problems are, in the cohomology theory of algebraic varieties.
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If Ais Hermitian, then we also have 1(A) 1(A) 1 n Xn i=1 a ii 2(A) n(A): Hence, for every Hermitian matrix A; 1(A) and 2(A) give equal or better bounds for, respectively, 1(A) and n(A) than trace(A) n: a matrix is not Hermitian then Theorem may apply to it and may not. For example, Theorem applies to C = 1 1 2 1.
Thats all. Now you can draw quadrics in OpenGL. Some really impressive things can be done with morphing and quadrics. The animated disc is an example of simple morphing.
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However, two distinct Hermitian varieties might intersect in many different configurations. Our aim in this thesis is to study such configurations in some detail. In Chapter 1 we introduce some background material on finite fields, projective spaces, collineation groups and Hermitian varieties.
Chapter 2 deals with the two-dimensional case. For a long time - at least from Fermat to Minkowski - the theory of quadratic forms was a part of number theory. Much of the best work of the great number theorists of the eighteenth and nineteenth century was concerned with problems about quadratic by: Show that eigenvalues of a Hermitian matrix are real numbers.
These two proofs are essentially the same. The second proof is a bit simpler and concise compared to the first one. Let be an arbitrary eigenvalue of a Hermitian matrix and let be an eigenvector corresponding to the eigenvalue.
The first equality follows because the dot product of.Consider the submanifold S 1 of Hp;q de ned by the formula Xp j=1 jzjj2 = pX+q j=p+1 jzjj2 = 1: (1) Then S 1 is the product of two spheres S 1 = S2p 1 S2q 1 and the projection P0 restricted to S 1 is a di eomorphism from S 1 to Q0= P0(Q):The representation of Q0as a product of two spheres will, in general, depend on the choice of the orthonormal basis, more speci cally: on the split .