In this paper, we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields and then apply them to construct LCD codes. Construction methods include random sampling in the orthogonal group, code extension, matrix product codes and projection over a self-dual basis.

Approximately dual frames are studied in the Hilbert space setting. Approximate duals are easier to construct than classical dual frames, and can be tailored to yield almost perfect reconstruction. Bounds on the deviation from perfect reconstruction are obtained for approximately dual frames constructed via perturbation theory. An alternative bound is derived for the rich class of Gabor frames,...

We extend strong/weak coupling duality to string theories without spacetime supersymmetry, and focus on the case of the unique ten-dimensional, nonsupersymmetric, tachyon-free SO(16)×SO(16) heterotic string. We construct a tachyon-free heterotic string model that interpolates smoothly between this string and the ten-dimensional supersymmetric SO(32) heterotic string, and we construct a dual for...

A series of monomial representations of SL2(p) is used to construct a new series of self-dual ternary codes of length 2(p + 1) for all primes p ≡ 5 (mod 8). In particular we find a new extremal self-dual ternary code of length 60.

In the first part of this paper, we implement the multiplier algebra of the dual of an algebraic quantum group (A, ∆) (see [13]) as a subset of the space of linear functionals on A. In a second part, we construct the universal corepresentation and use it to prove a bijective corespondence between corepresentations of (A, ∆) and homomorphisms on its dual.

In this article, we construct a Fenchel-Lagrangian ε-dual problem for set-valued optimization problems by using the perturbation methods. Some relationships between the solutions of the primal and the dual problems are discussed. Moreover, an ε-saddle point theorem is proved.

The Chern-Simons level k of ABJM gauge theory captures the orbifolding in the dual geometry. This suggests that if we move the membranes away from the tip of the orbifold to a smooth point, it should trigger an RG flow that changes the level to k = 1. We construct an explicit supergravity solution that is dual to this shift from generic k to k = 1. In the gauge theory side, we present arguments...

We construct particular Hamiltonian systems associated to graphs embedded in Euclidean n−dimensional space and apply the dual transformation to this system. This result extends the one-dimensional dual transformation associated to the Toda lattice. We also discuss some applications to solid state lattice theory.

The purpose of this note is to construct new self-dual codes over GF (7) of lengths 28 with the highest known minimum weights. We show the existence of at least 74 self-dual [28,14, 10] codes. Mathematics Subject Classification: 94B05