Type II Self-Dual Codes over Finite Rings and Even Unimodular Lattices

In this paper, we investigate self-dual codes over finite rings, specifically the ring of integers modulo 2m. Type II codes over are introduced as self-dual codes with Euclidean weights which are a multiple of 2m +1. We describe a relationship between Type II codes and even unimodular lattices. This relationship provides much information on Type II codes. Double circulant Type II codes over are also studied.     

Isodual Codes over ℤ2k and Isodual Lattices

A code is called isodual if it is equivalent to its dual code, and a lattice is called isodual if it is isometric to its dual lattice. In this note, we investigate isodual codes over _2k . These codes give rise to isodual lattices; in particular, we construct a 22-dimensional isodual lattice with minimum norm 3 and kissing number 2464.     

On some classes of linear codes over $${\mathbb {Z}}_{2}{\mathbb {Z}}_{4}$$ and their covering radii

In this paper, we define the simplex and MacDonald codes of types \(\alpha \) and \(\beta \) over \({\mathbb {Z}}_{2}{\mathbb {Z}}_{4}\). We also examine the covering radii of these codes. Further, we study the binary images of these codes and prove that the binary image of the simplex codes of type \(\alpha \) meets the Gilbert bound.     

On codes over $$\mathbb {F}_{q}+v\mathbb {F}_{q}+v^{2}\mathbb {F}_{q}$$

In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-dual codes over the ring \(R=\mathbb {F}_{q}+v\mathbb {F}_{q}+v^{2}\mathbb {F}_{q}\), where \(v^{3}=v\), for q odd. We give conditions on the existence of LCD codes and present construction of formally self-dual codes over R. Further, we give bounds on the minimum distance of LCD codes over \(\mathbb {F}_q\) and extend these to codes over R.     

New Good Rate (m-1)/pm Ternary and Quaternary Quasi-Cyclic Codes

Previous results have shown that the class of quasi-cyclic (QC) codes contains many good codes. In this paper, new rate (m - 1)/pm QC codes over GF(3) and GF(4) are presented. These codes have been constructed using integer linear programming and a heuristic combinatorial optimization algorithm based on a greedy local search. Most of these codes attain the maximum possible minimum distance for any linear code with the same parameters, i.e., they are optimal, and 58 improve the maximum known distances. The generator polynomials for these 58 codes are tabulated, and the minimum distances of rate (m - 1)/pm QC codes are given.     

Classification of Extremal Double Circulant Formally Self-Dual Even Codes

Formally self-dual even codes have recently been studied. Double circulant even codes are a family of such codes and almost all known extremal formally self-dual even codes are of this form. In this paper, we classify all extremal double circulant formally self-dual even codes which are not self-dual. We also investigate the existence of near-extremal formally self-dual even codes.     

Nonlinear optical and two-photon absorption properties of octupolar tris(bipyridyl)metal complexes

The linear (absorption and emission) and nonlinear optical (NLO) properties of a series of D(3) [(Fe(II), Ru(II), Ni(II), Cu(II), Zn(II)] octupolar metal complexes featuring the 4,4'-bis[(dibutylamino)styryl]-2,2'-bipyridine ligand are reported. Zinc(II), nickel(II), and copper(II) complexes exhibit similar absorption spectra in the visible region (lambda(ILCT) = 474-476 nm) which are assigned to intraligand charge-transfer (ILCT) bands. The quadratic and cubic NLO properties are strongly influenced by the nature of the metallic center. Harmonic light scattering studies at lambda = 1.91 microm reveal that these chromophores display large first hyperpolarizabilities beta(1.91) in the range of (211-340) x 10(-30) esu; replacing the Zn(II) metal ion by Ni(II) or Cu(II) results in a decrease of the static beta(0) coefficient by a factor of 1.5-1.6. Z-scan measurements at 765 and 965 nm reveal relatively large two-photon absorption cross-sections [650 < sigma(2) < 2200 GM], showing that both beta and sigma(2) values can be tuned by simple modification of the metal ion.     

The sharp isoperimetric inequality for minimal surfaces with radially connected boundary in hyperbolic space

Oblatum 15-X-1991 & 4-I-1992