CODES, COMPOSITIONS AND LATTICES

Universal codes and unimodular lattices

Binary quadratic residue codes of length p + 1 produce via construction B and density doubling type II lattices like the Leech. Recently, quaternary quadratic residue codes have been shown to produce the same lattices by construction A modulo 4. We prove in a direct way the equivalence of these two constructions for p ~ 31. In dimension 32, we obtain an extremal lattice of type II not isometric...

Codes and Lattices in Cryptography

We compare Schnorr's algorithm for semi block 2k-reduction of lattice bases with Koy's primal-dual reduction for blocksize 2k. Koy's algorithm guarantees within the same time bound under known proofs better approximations of the shortest lattice vector. Under reasonable heuristics both algorithms are equally strong and much better than proven in worst-case. We combine primal-dual reduction with...

Codes, Lattices, and Steiner Systems

Two classification schemes for Steiner triple systems on 15 points have been proposed recently: one based on the binary code spanned by the blocks, the other on the root system attached to the lattice affinely generated by the blocks. It is shown here that the two approaches are equivalent. 1991 AMS Classification: Primary: 05B07; Secondary: 11H06, 94B25.

Betweeen Codes and Lattices: Hybrid lattices and the NTWO cryptosystem

On identifying codes in lattices

Let G(V,E) be a simple, undirected graph. An identifying code on G is a vertex-subset C ⊆ V such that B(v) ∩ C is non-empty and distinct for each vertex v ∈ V , where B(v) is a ball about v. Motivated by applications to fault diagnosis in multiprocessor arrays, a number of researchers have considered the problem of constructing identifying codes of minimum density on various two-dimensional lat...