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In this study, we consider the Euclidean and Galois hulls of multi-twisted (MT) codes over a finite field $\mathbb{F}_{p^e}$ of characteristic $p$. Let $\mathbf{G}$ be a generator polynomial matrix (GPM) of a MT code $\mathcal{C}$. For any $0\le \kappa

Contaminants reduction in Electron Cyclotron Resonance Charge Breeders (ECRCB) is a key point for the future experiments foreseen at LNL and GANIL Isotope Separation On Line (ISOL) facilities. According to the mass separator resolution set downstream the ECRCB, the radioactive ion beam study can be challenged in case of low production rate. An ongoing collaboration between LNL, LPSC and GANIL laboratories aims to improve the beam purity, acting on all the pollutant causes. Comparative experiments will be done at LPSC using different techniques, like covering the plasma chamber wall with liners of different materials. Different configurations of the ECRCB will also be tested, with the enhancement of the efficiency and charge breeding time parameters as additional objectives. A presentation of this program is proposed together with the recent upgrade of the LPSC 1+N+ test bench, with the aim to improve the vacuum quality., Proceedings of the 24th International Workshop on ECR Ion Sources, ECRIS2020, East Lansing, MI, USA

SEISM is a compact ECR ion source operating at 60 GHz developed up to 2014. The prototype uses a magnetic cusp to confine the plasma. This simple magnetic geometry was chosen to allow the use of polyhelix coils (developed at the LNCMI, Grenoble) to generate a strong magnetic confinement featuring a closed ECR surface at 2.1 T. The plasma is sustained by a 300 kW microwave pulse of 1 ms duration and with a 2 Hz repetition rate. Previous experiments at LNCMI have successfully demonstrated the establishment of the nominal magnetic field and the extraction of ion beams with a current density up to ~ 1A/cm². The presence of "afterglow" peaks was also observed, proving the existence of ion confinement in a cusp ECR ion source. The last run was prematurely stopped but the project restarted in 2018 and new experiments are planned in 2021. A new transport beam line has been designed to improve ion beam transport towards the beam detectors. Short- and long-term research plans are presented, including numerical simulations of the beam transport line and future upgrades of the ion source with the main goal to transform the high current density measured into a real high intensity ion beam., Proceedings of the 24th International Workshop on ECR Ion Sources, ECRIS2020, East Lansing, MI, USA

Linear codes with complementary-duals (LCD) are linear codes that intersect with their dual trivially. Multinegacirculant codes of index $2$ that are LCD are characterized algebraically and some good codes are found in this family. Exact enumeration is performed for indices 2 and 3, and for all indices $t$ for a special case of the co-index by using their concatenated structure. Asymptotic existence results are derived for the special class of such codes that are one-generator and have co-index a power of two by means of Dickson polynomials. This shows that there are infinite families of LCD multinegacirculant codes with relative distance satisfying a modified Varshamov-Gilbert bound., arXiv admin note: text overlap with arXiv:1606.00815

International audience; We construct trace codes over Z 4 based on Boolean functions and their support. The Lee weight distribution of these codes is studied by using the Walsh-Hadamard transform of the Boolean functions, and exponential character sums. We obtain few weights codes. In particular, bent and semi-bent functions give three-weight codes.

International audience; Upper and lower bounds on the largest number of weights in a cyclic code of given length, dimension and alphabet are given. An application to irreducible cyclic codes is considered. Sharper upper bounds are given for the special cyclic codes (called here strongly cyclic), whose nonzero codewords have period equal to the length of the code. Asymptotics are derived on the function Γ(k, q), that is defined as the largest number of nonzero weights a cyclic code of dimension k over F q can have, and an algorithm to compute it is sketched. The nonzero weights in some infinite families of Reed-Muller codes, either binary or q-ary, as well as in the q-ary Hamming code are determined, two difficult results of independent interest.

Electron cyclotron resonance charge breeder (ECR CB) is one of the instruments used to boost the radioactive ion beam (RIB) charge state in isotope separator on-line (ISOL) facilities. While the ECR CB can manage intense 1+ RIB without difficulty, the present CB generation co extracts significant amounts of impurities which can be detrimental to the study of very low intensity N+ RIB in today facilities if no downstream high mass resolution separation is available. This work investigates the im-provements achievable with a new generation 18 GHz ECR CB applicable to future facility like EURISOL. The study shows that with a modified ion source geometry, an optimized magnetic confinement, a careful wall metal choice like beryllium, a UHV vacuum technology, the charge breeder performance will improve as follows: 20 % higher capture efficiency, -40% charge breeding time, charge state ion production with mass over charge of 3 up to xenon and over 6 up to uranium, co-extracted contam-inant density reduction by a factor 60 to 600. An 18 GHz ECR CB ion source layout is finally proposed for EURISOL., Proceedings of the 23th Int. Workshop on ECR Ion Sources, ECRIS2018, Catania, Italy

In this paper, we construct an infinite family of five-weight codes from trace codes over the ring $R=\mathbb{F}_2+u\mathbb{F}_2$, where $u^2=0.$ The trace codes have the algebraic structure of abelian codes. Their Lee weight is computed by using character sums. Combined with Pless power moments and Newton's Identities, the weight distribution of the Gray image of trace codes was present. Their support structure is determined. An application to secret sharing schemes is given., 14 pages, need help in page 12. arXiv admin note: text overlap with arXiv:1612.00966

In this paper we find a complete characterization of plateaued Boolean functions in terms of the associated Cayley graphs. Precisely, we show that a Boolean function $f$ is $s$-plateaued (of weight $=2^{(n+s-2)/2}$) if and only if the associated Cayley graph is a complete bipartite graph between the support of $f$ and its complement (hence the graph is strongly regular of parameters $e=0,d=2^{(n+s-2)/2}$). Moreover, a Boolean function $f$ is $s$-plateaued (of weight $\neq 2^{(n+s-2)/2}$) if and only if the associated Cayley graph is strongly $3$-walk-regular (and also strongly $\ell$-walk-regular, for all odd $\ell\geq 3$) with some explicitly given parameters., 7 pages, 1 figure, Proceedings of Africacrypt 2018

We study trace codes with defining set $L,$ a subgroup of the multiplicative group of an extension of degree $m$ of the alphabet ring $\mathbb{F}_3+u\mathbb{F}_3+u^{2}\mathbb{F}_{3},$ with $u^{3}=1.$ These codes are abelian, and their ternary images are quasi-cyclic of co-index three (a.k.a. cubic codes). Their Lee weight distributions are computed by using Gauss sums. These codes have three nonzero weights when $m$ is singly-even and $|L|=\frac{3^{3m}-3^{2m}}{2}.$ When $m$ is odd, and $|L|=\frac{3^{3m}-3^{2m}}{2}$, or $|L|={3^{3m}-3^{2m}}$ and $m$ is a positive integer, we obtain two new infinite families of two-weight codes which are optimal. Applications of the image codes to secret sharing schemes are also given., 11 pages, submitted on 2 December. arXiv admin note: text overlap with arXiv:1612.00118

Primary ion beams from metallic elements are routinely produced at GANIL using ECR4 and ECR4M 'room temperature' ECR ion sources. Ionization efficiency measurements, partially presented in the past, are summarized in this report together with updated and new results obtained with Cd, Mo and Ta. Preliminary results for Ni and Ca obtained with the room temperature Phoenix-V2 ECR ion source, under commissioning for SPIRAL 2, are also included. These ionization efficiencies are compared according to the production methods: oven, sputtering, MIVOC, gaseous compounds. The presently SPIRAL 2 heavy ion injector designed for ions Q/A=1/3 shows clear limitations in terms of intensity for metallic ions with mass higher than 60 (intensity < 1 pμA). In order to choose the best ion source for a future Q/A=1/6, 1/7 injector, best world results have been compiled for different existing 'room temperature' and superconducting ECR ion sources., Proceedings of the 22nd Int. Workshop on ECR Ion Sources, ECRIS2016, Busan, Korea