Paper Info
Title
On Quadratic Residue Codes And Hyperelliptic Curves
Abstract
For an odd prime p and each non-empty subset S subset of GF (p), consider the hyperelliptic curve X-S defined by y(2) = f(S) (x), where f(S) (x) = Pi (a is an element of S) (x - a). Using a connection between binary quadratic residue codes and hyperelliptic curves over GF (p), this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S subset of GF (p) for which the bound vertical bar X-S (GF (p))vertical bar > 1.39p holds. We also use the quasi-quadratic residue codes defined below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the "Riemann hypothesis.".
Year
Venue
Keywords
2008
DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
binary linear codes, hyperelliptic curves over a finite field, quadratic residue codes, (11T71, 11T24, 14G50, 94B40, 94B27)
DocType
Volume
Issue
Journal
10
1
ISSN
Citations 
PageRank 
1365-8050
2
0.47
References 
Authors
4
1
Name
Order
Citations
PageRank
David Joyner198.40