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Tate Pairing Implementation for Hyperelliptic Curves y2 = xp-x + d
A closed formula is given for the Tate pairing on the hyperelliptic curve y 2 = x p – x + d in characteristic p in order to improve the implementations in [BKLS02], [GHS02] for the special case p=3. Expand
Speeding up the Discrete Log Computation on Curves with Automorphisms
We show how to speed up the discrete log computations on curves having automorphisms of large order, thus generalizing the attacks on anomalous binary elliptic curves. This includes the first knownExpand
Extremal weight enumerators and ultraspherical polynomials
  • I. Duursma
  • Computer Science, Mathematics
  • Discret. Math.
  • 6 July 2003
An upper bound for the minimum distance of a divisible code in terms of its dual distance is established and the zeta function of a quaternary extremal self-dual code has its zeros on the circle |T|=q^-^1^/^2 in analogy with the zets of an algebraic curve. Expand
Majority coset decoding
  • I. Duursma
  • Mathematics, Computer Science
  • IEEE Trans. Inf. Theory
  • 1 May 1993
A majority coset decoding (MCD) procedure that can be applied to an arbitrary geometric code is discussed and a strictly smaller cost containing the error vector is obtained. Expand
Repairing Reed-Solomon Codes With Multiple Erasures
A single erasure repair method for RS codes that achieves the optimal repair bandwidth amongst all linear encoding schemes is proposed and the trace collection technique is extended to cope with two and three erasures. Expand
Weight distributions of geometric Goppa codes
The in general hard problem of computing weight distributions of linear codes is considered for the special class of algebraic-geometric codes, defined by Goppa in the early eighties. Known resultsExpand
Efficient algorithms for the Jacobian variety of hyperelliptic curves $y^2=x^p-x+1$ over a finite field of odd characteristic $p$
We develop efficient algorithms for the Jacobian of the hyperelliptic curve defined by the equation y2=xp-x+1 over a finite field F p n of odd characteristic p. We first determine the zeta functionExpand
Combinatorics of the Two-Variable Zeta Function
  • I. Duursma
  • Computer Science
  • International Conference on Finite Fields and…
  • 5 May 2003
The rank polynomial of a matroid is considered and some well-known applications to graphs and linear codes are mentioned, and a relation for algebraic-geometric codes between the matroid of a code and the two-variable zeta function of a curve is compared. Expand
Tate-pairing implementations for tripartite key agreement
Error-locating pairs for cyclic codes
A general decoding method for linear codes is investigated for cyclic codes, and a new family of codes is given for which the decoding needs only O(n/sup 2/) operations. Expand