We show that regular homogeneous two-weight Z pk -codes where p is odd and k > 2 with dual Hamming distance at least four do not exist. The proof relies on existence conditions for the strongly regular graph built on the cosets of the dual code.

We describe in purely combinatorial terms dual pairs of integral affine structures on spheres which come from the conjectural metric collapse of mirror families of Calabi-Yau toric hypersurfaces. The same structures arise on the base of a special Lagrangian torus fibration in the Strominger-Yau-Zaslow conjecture. We study the topological torus fibration in the large complex structure limit and ...

The MacWilliams identity, which relates the weight distribution of a code to the weight distribution of its dual code, is useful in determining the weight distribution of codes. In this paper, we derive the MacWilliams identity for linear codes with the rank metric, and our identity has a different form than that by Delsarte. Using our MacWilliams identity, we also derive related identities for...

Let T be a torus over an algebraically closed field k of characteristic 0, and consider a projective T -module P(V ). We determine when a projective toric subvariety X ⊂ P(V ) is self-dual, in terms of the configuration of weights of V .

A computer calculation with Magma shows that there is no extremal self-dual binary code C of length 72 whose automorphism group contains the symmetric group of degree 3, the alternating group of degree 4 or the dihedral group of order 8. Combining this with the known results in the literature one obtains that Aut(C) has order at most 5 or is isomorphic to the elementary abelian group of order 8.

Multivariate hypergeometric functions associated with toric varieties were introduced by Gel’fand, Kapranov and Zelevinsky. Singularities of such functions are discriminants, that is, divisors projectively dual to torus orbit closures. We show that most of these potential denominators never appear in rational hypergeometric functions. We conjecture that the denominator of any rational hypergeom...

This paper studies the problem of register allocation and scheduling for Dual-Load-Execute (DLE) architectures. These are architectures which can execute an ALU instruction and two memory transfer operations (load/store) in a single instruction cycle. DLE architectures are extensively used in the design of Digital Signal Processors (DSPs) like the Motorola 56000, Analog Devices ADSP-2100, and N...