We prove a formula for the minimum distance of two-point codes on a Hermitian curve.
For a given curve X and divisor class C, we give lower bounds on the degree of a divisor A such that A and A − C belong to specified semigroups of divisors. For suitable choices of the semigroups we obtain (1) lower bounds for the size of a party A that can recover the secret in an algebraic geometric linear secret sharing scheme with adversary threshold C,… (More)
Various methods have been used to obtain improvements of the Goppa lower bound for the minimum distance of an algebraic geometric code. The main methods divide into two categories and all but a few of the known bounds are special cases of either the Lundell-McCullough floor bound or the Beelen order bound. The exceptions are recent improvements of the floor… (More)
In , the authors formulate new coset bounds for algebraic geometric codes. The bounds give improved lower bounds for the minumum distance of algebraic geometric codes as well as improved thresholds for algebraic geometric linear secret sharing schemes. The coset bounds depend on the choice of a sequence of divisors and on its intersection with a given… (More)
We generalize the ElGamal signature scheme for cyclic groups to a signature scheme for n-dimensional vector spaces. The higher dimensional version is based on the untractability of the vector decomposition problem (VDP). Yoshida has shown that under certain conditions, the VDP on a two-dimensional vector space is at least as hard as the computational… (More)