Maximal values of generalized algebraic immunity

The notion of algebraic immunity of Boolean functions has been generalized in several ways to vector-valued functions and/or over arbitrary finite fields and reasonable upper bounds for such generalized algebraic immunities has been proved in Armknecht and Krause (Proceedings of ICALP 2006, LNCS, vol. 4052, pp 180–191, 2006), Ars and Faugere (Algebraic immunity of functions over finite fields, INRIA, No report 5532, 2005) and Batten (Canteaut, Viswanathan (eds.) Progress in Cryptology—INDOCRYPT 2004, LNCS, vol. 3348, pp 84–91, 2004). In this paper we show that the upper bounds can be reached as the maximal values of algebraic immunities for most of generalizations by using properties of Reed–Muller codes.      

A lower bound for the minimum weight of the dual 7-ary code of a projective plane of order 49

Existing bounds on the minimum weight d ^⊥ of the dual 7-ary code of a projective plane of order 49 show that this must be in the range 76 ≤ d ^⊥ ≤ 98. We use combinatorial arguments to improve this range to 88 ≤ d ^⊥ ≤ 98, noting that the upper bound can be taken to be 91 if the plane has a Baer subplane, as in the desarguesian case. A brief survey of known results for the minimum weight of the dual codes of finite projective planes is also included. Dedicated to Dan Hughes on the occasion of his 80th birthday.     

Sequential and dynamic frameproof codes

There are many schemes in the literature for protecting digital data from piracy by the use of digital fingerprinting, such as frameproof codes and traitor-tracing schemes. The concept of traitor-tracing has been applied to a digital broadcast setting in the form of dynamic traitor-tracing schemes and sequential traitor-tracing schemes, which could be used to combat piracy of pay-TV broadcasts, for example. In this paper, we extend the properties of frameproof codes to this dynamic model, defining and constructing both l-sequential c-frameproof codes and l-dynamic c-frameproof codes. We also give bounds on the number of users supported by such schemes.      

Extremal Kähler metrics and Bach–Merkulov equations

In this paper, we study a coupled system of equations on oriented compact 4-manifolds which we call the Bach–Merkulov equations. These equations can be thought of as the conformally invariant version of the classical Einstein–Maxwell equations. Inspired by the work of C. LeBrun on Einstein–Maxwell equations on compact Kähler surfaces, we give a variational characterization of solutions to Bach–Merkulov equations as critical points of the Weyl functional. We also show that extremal Kähler metrics are solutions to these equations, although, contrary to the Einstein–Maxwell analogue, they are not necessarily minimizers of the Weyl functional. We illustrate this phenomenon by studying the Calabi action on Hirzebruch surfaces.     

Extremal solutions of second order impulsive dynamic equations on time scales

In this paper, we give an existence theorem for the extremal solutions for second order impulsive dynamic equations on time scales.     

广义Hamming重量与码的半线性等价

设σ是域F/b的一个自同构,该文证明两个线性码之间的任一保持一个 广义Hamming重量的σ-半线性同构是一个σ-半线性单项等价.     

Accelerator driven systems from the radiological safety point of view

In the proposed accelerator driven systems (ADS) the possible use of several milliamperes of protons of about 1 GeV incident on high mass targets like the molten lead-bismuth eutectic is anticipated to pose radiological problems that have so far not been encountered by the radiation protection community. Spallation reaction products like high energy gammas, neutrons, muons, pions and several radiotoxic nuclides including Po-210 complicate the situation. In the present paper, we discuss radiation safety measures like bulk shielding, containment of radiation leakage through ducts and penetration and induced activity in the structure to protect radiation workers as well as estimation of sky-shine, soil and ground water activation, release of toxic gases to the environment to protect public as per the stipulations of the regulatory authorities. We recommend the application of the probabilistic safety analysis technique by assessing the probability and criticality of different hazard-initiating events using HAZOP and FMECA.      

环F2＋uF2上偶长的（1＋u）-常循环码

给出了环F2＋uF2上任意偶长的（1＋u）-常循环码的结构，确定了给定偶长度F2＋uF2上（1＋u）-常循环码的数目．通过Gray映射，得到了F2＋uF2上偶长的（1＋u）-常循环码的二元象．