Linear codes from support designs of ternary cyclic codes

Designs, Codes and Cryptography - For a long time, the literature has demonstrated that designs and codes are exciting topics for combinatorics and coding theory. Linear codes and t-designs are, in...     

Good polynomials for optimal LRC of low locality

Designs, Codes and Cryptography - According to a magnific method due to I. Tamo and A. Barg, a class of polynomials over finite fields, called good polynomials, was introduced and used to construct...     

Isolated-palladium complexes for catalyzed telomerization of butadiene with methanol in the presence of water

In order to study the performance of organometallic complexes in the telomerization of butadiene with methanol in aqueous medium, we synthesized and characterised hydrosoluble palladium complexes. [(π-allyl)Pd(TPPTS)₂]⁺Cl⁻ complex exhibited strong stability as no degradation was observed after storage at room temperature under air atmosphere for weeks. TON’s up to 36 000 were achieved at 50 °C.     

Hypoelliptic non-homogeneous diffusions

 Let be a time dependent second order operator, written in usual or H?rmander form. We study the regularity of the law of the associated non-homogeneous (time dependent) diffusion process, under H?rmander's like conditions. Coefficients are only H?lder continuous in time. The main tool is Malliavin calculus. Our results extend and correct previous ones ([17] and related works, [15]). Related topics like filtering theory, killed or reflected processes, parabolic hypoellipticity are also discussed. Received: October 1999/Revised version: 12 November 2001 / Published online: 1 July 2002     

Synthesis of diethyl 2-(aryl)vinylphosphonates by the Heck reaction catalysed by well-defined palladium complexes

Pd-catalysed procedures for the direct Heck arylation of diethyl vinylphosphonate with various aryl or heteroaryl halides toward the synthesis of diethyl 2-(aryl)vinylphosphonates are reported. Several homogeneous catalytic systems (i.e. Herrmann palladacycle, Nolan (NHC)-palladium catalyst, Pd(OAc)₂/PPh₃) were used and compared within the study. High conversions and selectivities were achieved under optimised conditions (2 mol% [Pd], NMP, K₂CO₃, 140 °C) whatever the homogeneous catalyst used.     

On the <Emphasis Type="Italic">p</Emphasis>-ary (cubic) bent and plateaued (vectorial) functions

Plateaued functions play a significant role in cryptography, sequences for communications, and the related combinatorics and designs. Comparing to their importance, those functions have not been studied in detail in a general framework. Our motivation is to bring further results on the characterizations of bent and plateaued functions, and to introduce new tools which allow us firstly a better understanding of their structure and secondly to get methods for handling and designing such functions. We first characterize bent functions in terms of all even moments of the Walsh transform, and then plateaued (vectorial) functions in terms of the value distribution of the second-order derivatives. Moreover, we devote to cubic functions the characterization of plateaued functions in terms of the value distribution of the second-order derivatives, and hence this reveals non-existence of homogeneous cubic bent (and also (homogeneous) cubic plateaued for some cases) functions in odd characteristic. We use a rank notion which generalizes the rank notion of quadratic functions. This rank notion reveals new results about (homogeneous) cubic plateaued functions. Furthermore, we observe non-existence of a function whose absolute Walsh transform takes exactly 3 distinct values (one being zero). We finally provide a new class of functions whose absolute Walsh transform takes exactly 4 distinct values (one being zero).     

A new class of bent and hyper-bent Boolean functions in polynomial forms

Bent functions are maximally nonlinear Boolean functions and exist only for functions with even number of inputs. This paper is a contribution to the construction of bent functions over ${\mathbb{F}_{2^{n}}}$ (n = 2m) having the form ${f(x) = tr_{o(s_1)} (a x^ {s_1}) + tr_{o(s_2)} (b x^{s_2})}$ where o(s _i ) denotes the cardinality of the cyclotomic class of 2 modulo 2 ⁿ ? 1 which contains s _i and whose coefficients a and b are, respectively in ${F_{2^{o(s_1)}}}$ and ${F_{2^{o(s_2)}}}$ . Many constructions of monomial bent functions are presented in the literature but very few are known even in the binomial case. We prove that the exponents s ₁ = 2 ^m ? 1 and ${s_2={\frac {2^n-1}3}}$ , where ${a\in\mathbb{F}_{2^{n}}}$ (a ?? 0) and ${b\in\mathbb{F}_{4}}$ provide a construction of bent functions over ${\mathbb{F}_{2^{n}}}$ with optimum algebraic degree. For m odd, we give an explicit characterization of the bentness of these functions, in terms of the Kloosterman sums. We generalize the result for functions whose exponent s ₁ is of the form r(2 ^m ? 1) where r is co-prime with 2 ^m  + 1. The corresponding bent functions are also hyper-bent. For m even, we give a necessary condition of bentness in terms of these Kloosterman sums.     

Correction to: Good polynomials for optimal LRC of low locality

Designs, Codes and Cryptography -