In this paper, we propose the construction of two code generators for optical ZCZ codes of Zcz = 4n−2 with positive n and Zcz = 1 using the Sylvester-type Hadamard matrix, which are called ROM-type and non ROM-type code generators. The optical ZCZ code is a set of pairs of binary and bi-phase sequences with zero correlation zone. An optical code division multiple access (CDMA) system using opti...

Given a renormalizable theory we construct the dilatation operator, in the sense of generator of RG flow of composite operators. The generator is found as a differential operator acting on the space of normal symbols of composite operators in the theory. In the spirit of AdS/CFT correspondence, this operator is interpreted as the Hamiltonian of the dual theory. In the case of a field theory wit...

GRAPE-Dilepton is a Monte Carlo event generator for dilepton production in ep collisions. The cross-section calculation is based on the exact matrix elements in the electroweak theory at tree level. The dilepton productions via γγ, γZ, ZZ collisions and via photon internal conversion are taken into account. In addition, the effects of the Z on/offshell production are also included. The relevant...

We present an efficient new method of obtaining a generator matrix G from certain types of parity check matrices with a defective cyclic block structure. This novel approach describes parity check and generator matrices in terms of polynomials. Moreover, by using this polynomial algebra we have found efficient ways to implement the scheme. In addition, this method is as such interesting as it a...

We begin a study of higher-loop corrections to the dilatation generator of N = 4 SYM in non-compact sectors. In these sectors, the dilatation generator contains infinitely many interactions, and therefore one expects very complicated higher-loop corrections. Remarkably, we find a short and simple expression for the two-loop dilatation generator. Our solution for the non-compact su(1, 1|2) secto...

State symmetries are defined as permutations which act on vector spaces of column vectors and square matrices, resulting in isotropy groups for specific vector spaces. A large number of properties for such objects is shown, to provide a rigorous basis for future applications. The main statement characterises the state symmetry of vector sequences (v) which are generated by powers of a generator...

The paper presents the next step on the complete classification of all optimal binary selfdual codes of length 52 that possess an automorphism of odd prime order. Applying the method for constructing binary self-dual codes with an automorphism of odd prime order p=3 we give full classification of all [52, 26, 10] binary self-dual codes with an automorphism of type 3-(16,4) for the next unsolved...

The generalized Hamming weight played an important role in coding theory. In the study of the wiretap channel of type 11, the generalized Hamming weight was extended to a two-code format. Two . equivalent concepts of the generalized Hamming weight hierarchy and its two-code format, are the inverse dimension/length profile (IDLP) and the inverse relative dimension/length profile (IRDLP), respect...

In this paper, rate 1/p binary systematic quasi-cyclic (QC) codes are constructed based on Matroid Theory (MT). The relationship between the generator matrix and minimum distance d is derived through MT, which is benefit to find numbers of QC codes with large minimum distance by our Matroid search algorithm. More than seventy of QC codes that extend previously published results are presented. A...

In this article we describe simulations of the hadronic decay of Higgs bosons produced in association with vector bosons at linear and hadronic colliders. We use the Monte Carlo at next-to-leading-order (MC@NLO) matching prescription with the Herwig++ event generator to predict various spectra of the resulting bb̄ pairs and compare our results with leading order and matrix element correction pre...