Arithmetic, Geometry, and Coding Theory: Proceedings of the International Conference held at Centre International de Rencontres de Mathématiques (CIRM), Luminy, France, June 28 - July 2, 1993R. Pellikaan, M. Perret, S.G. Vladut The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications. |
Contents
| 1 | |
| 9 | |
MDS codes from hyperelliptic curves | 23 |
On hypersurfaces defined by a separated variables polynomial over a finite field | 35 |
Class numbers for some hyperelliptic curves | 45 |
Generalized Hamming weights for duals of BCH codes and maximal algebraic function fields | 53 |
On the Clifford defect for special curves | 67 |
Number of points of plane sections and linear codes defined on algebraic varieties | 77 |
On special divisors and the two variable zeta function of algebraic curves over finite fields | 175 |
Minoration de certaines sommes exponentielles II | 185 |
Dénombrement des configurations dans le plan projectif | 199 |
Nombre de points des surfaces sur un corps fini | 209 |
Algebraic curves and sphere packings | 225 |
Two remarks on spectra of algebraic geometry codes | 253 |
An upper bound for generalized Hamming weights | 263 |
Generalized Hamming weights Fundamental open problems in coding theory | 269 |
Quadratic algebraic function fields with ideal class number two | 105 |
A survey of Ramanujan graphs | 127 |
Codes associated to Grassmannians | 145 |
The shift bound for cyclic ReedMuller and geometric Goppa codes | 155 |
List of Contributors | 283 |
List of Participants | 287 |
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Common terms and phrases
algebraic function fields algebraic geometry algebraic number field algebraic-geometric codes algorithm asymptotic b₁ b₂ BCH codes class number coding theory complete defining set compute configuration conjecture Corollary coset decoding Definition deg(ƒ deg(h denote dim Sing dimension divisor class eigenvalues Example exists F₁ finite field genus g Goppa codes Hamming weights hyperelliptic curves hyperelliptic function hyperelliptic function field hyperplane hypersurface IEEE Trans independent with respect integers irreducible isomorphic lattice Lemma linear codes log₂ Math Mathematics Subject Classification matrix maximal MDS codes minimum distance n₁ nombre nondegenerate number field number of points obtain P₁ packing parameters peut polynomial Proof Proposition r-dimensional R₁ Ramanujan graphs ramifies rational points Reed-Muller codes result Riemann hypothesis Section semigroup sequence shift bound subcode subset subspace Theorem théorème trace codes Tsfasman variable zeta function variétés vector weight hierarchy zeros