Last edited by Arashizragore

Monday, April 27, 2020 | History

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

- 60 Want to read
- 2 Currently reading

Published
**1966** by Research and Training School, Indian Statistical Institute in Calcutta .

Written in English

- Finite geometries.,
- Error-correcting codes (Information theory)

**Edition Notes**

Statement | by R. C. Bose. |

Series | Indian Statistical Institute. Research and Training School. Mimeographed ser., publication no. M 66-1 |

Contributions | Ramanujacharyulu, C. |

Classifications | |
---|---|

LC Classifications | QA167.2 .B67 |

The Physical Object | |

Pagination | iii, 144 p. |

Number of Pages | 144 |

ID Numbers | |

Open Library | OL5031564M |

LC Control Number | 73900538 |

Robert D.M. Accola The book's main concern is automorphisms of Riemann surfaces, giving a foundational treatment from the point of view of Galois coverings, and treating the problem of the largest automorphism group for a Riemann surface of a given genus. In addition, the extent to which fixed points of automorphisms are generalized Weierstrass points is considered. Come to the Pizza Seminar this Wednesday to see that "What this really is, is one of the purest illustrations I've seen in my career of the power and glory of the P ≠NP phenomenon. The ratio of the difficulty of finding the proof to the difficulty of completely grasping it is in the hundreds of thousands or millions. Data Structures | Binary Trees | Question 10 A complete n-ary tree is a tree in which each node has n children or no children. Let I be the number of internal nodes and L be the number of leaves in a complete n-ary tree. Suppose a 2x2 matrix X (not necessarily hermitian, nor unitary) is written as X = a0 + sigma. a (the sigma. a is a dot product between sigma and a) where a0 and a1, a2 and a3 are numbers. How on earth does X represent a matrix? it's a number added to another number (dot product). Homework Equations The Attempt at a Solution.

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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 and Its Applications, vol Springer, New Cited by: Functional codes arising from quadric intersections with Hermitian varieties A.

Hallez L. Storme Hermitian varieties Abstract We investigate the functional code C h(X) introduced by G. Lachaud [10] 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 [2], 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, Quadrics 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 [1], 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.

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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. Everyone if you have time go check out my website, GB Schmick (TipTup) Jeff Molofee (NeHe) * DOWNLOAD Visual C++ Code For This Lesson. Thanks for contributing an answer to Mathematics Stack Exchange. Please be sure to answer the question.

Provide details and share your research. But avoid Asking for help, clarification, or responding to other answers. Making statements based on opinion; back them up with references or personal experience. Use MathJax to format equations. 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.

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We present some lower bounds for the Frobenius condition number of a positive definite matrix depending on trace, determinant, and Frobenius norm of a positive definite matrix and compare these results with other results. Also, we give a relation for the cosine of the angle between two given real by: 3.

A Hermitian matrix (or self-adjoint matrix) is one which is equal to its Hermitian adjoint (also known as its conjugate transpose). Every entry in the transposed matrix is equal to the complex conjugate of the corresponding entry in the original matrix.

or in matrix notation: where A T stands for A transposed. In physics the dagger symbol is often used instead of the star. Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

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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.

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less) hermitian matrices: Leta = exp(7Tî/«) and let 7denote the «X«identity. If ai = MiM2Mz, where the M,- are hermitian, then aMr1 is similar to its adjoint; hence a2Mi-1 and Mi~l are similar and have the same spectrum.

This is a contradiction since Mc1 is her-mitian and a2 is nonreal. Now A T = => A is Hermitian (the ij-element is conjugate to the ji-element).Since A is Hermitian, we have A H = A = diagonal elements of a Hermitian matrix are real.

Comments: 20 pages, 16 figures. Reported in several conferences, cf.: "International workshop in Singularity Theory, its Applications ad futur prospects. Liverpool, June " "Workshop on Singularities in geometry, topology, foliations and dynamics.

Solve for y in terms of x. To find the inverse, switch x and y, and solve for y. Multiply through by 4. This expression is the inverse of the given expression. Already have an account?. Identify the errors made in finding the inverse of y = x2 + 12x.

Describe the three errors. Get the answers you need, now!CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We study ecient iterative methods for the large sparse non-Hermitian positive de nite system of linear equations based on the Hermitian and skew-Hermitian splitting of the coecient matrix.

These methods include a Hermitian/skew-Hermitian splitting (HSS) iteration and its inexact variant, the inexact .Quantiki Quantum Information Portal and Wiki. Hermitian matrix. Let M n be the set of n × n complex-valued matrices. Let us consider a matrix A = [a ij] ∈ M n and denote its complex conjugate by $\; \overline{A}=[\overline{a}_{ij}]$ and its transpose by A .