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We give a complete classification of completely regular self-dual codes with covering radius $\rho = 2$. More precisely, we prove that there are two sporadic such codes, of length $8$, and an infinite family, of length $4$. We provide a description of all such codes and give the intersection arrays for all of them.

We classify all linear completely regular codes which have covering radius $\rho = 2$ and whose dual are antipodal. For this, we firstly show several properties of such dual codes, which are two-weight codes.

We consider $q$-ary (linear and nonlinear) block codes with exactly two distances: $d$ and $d+\delta$. Several combinatorial constructions of optimal such codes are given. In the linear (but not necessary projective) case, we prove that under certain conditions the existence of such linear $2$-weight code with $\delta > 1$ implies the following equality of great common divisors: $(d,q) = (\delta,q)$. Upper bounds for the maximum cardinality of such codes are derived by linear programming and from few-distance spherical codes. Tables of lower and upper bounds for small $q = 2,3,4$ and $q\,n < 50$ are presented., Comment: submitted

The experiment Neutrino-4 had started in 2014 with a detector model and then was continued with a full-scale detector in 2016 - 2021. In this article we describe all steps of preparatory work on this experiment. We present all results of the Neutrino-4 experiment with increased statistical accuracy provided to date. The experimental setup is constructed to measure the flux and spectrum of the reactor antineutrinos as a function of distance to the center of the active zone of the SM-3 reactor (Dimitrovgrad, Russia) in the range of 6 - 12 meters. Using all the collected data, we performed a model-independent analysis to determine the oscillation parameters $\Delta m_{14}^2$ and $\sin^22\theta_{14}$. The method of coherent summation of measurement results allows to directly demonstrate the oscillation effect. We present the analysis of possible systematic errors and the MC model of the experiment, which considers the possibility of the effect manifestation at the present precision level. As a result of the analysis, we can conclude that at currently available statistical accuracy we observe the oscillations at the $2.9\sigma$ level with parameters $\Delta m_{14}^2=(7.3\pm0.13_{st}\pm1.16_{sys})\text{eV}^2 = (7.3\pm1.17)\text{eV}^2$ and $\sin^22\theta_{14}= 0.36\pm0.12_{stat}(2.9\sigma)$. Monte Carlo based statistical analysis gave estimation of confidence level at $2.7\sigma$. We plan to improve the currently working experimental setup and create a completely new setup in order to increase the accuracy of the experiment by 3 times. We also provide a brief analysis of the general experimental situation in the search for sterile neutrinos., Comment: 38 pages, 54 figures. arXiv admin note: text overlap with arXiv:2003.03199, arXiv:1809.10561

The $q$-ary block codes with two distances $d$ and $d+1$ are considered. Several constructions of such codes are given, as in the linear case all codes can be obtained by a simple modification of linear equidistant codes. Upper bounds for the maximum cardinality of such codes is derived. Tables of lower and upper bounds for small $q$ and $n$ are presented., Comment: 12 pages

Given a parity-check matrix $H_m$ of a $q$-ary Hamming code, we consider a partition of the columns into two subsets. Then, we consider the two codes that have these submatrices as parity-check matrices. We say that anyone of these two codes is the supplementary code of the other one. We obtain that if one of these codes is a Hamming code, then the supplementary code is completely regular and completely transitive. If one of the codes is completely regular with covering radius $2$, then the supplementary code is also completely regular with covering radius at most $2$. Moreover, in this case, either both codes are completely transitive, or both are not. With this technique, we obtain infinite families of completely regular and completely transitive codes which are quasi-perfect uniformly packed.

We present the results of the Neutrino-4 experiment on search for a sterile neutrino. The experiment has been carried out on the SM-3 reactor having a compact active zone of $42\times42\times35\textrm{cm}^3$ and operating on the highly enriched uranium-235 at 90 MW thermal power. We report the results of the Neutrino-4 experiment of measurements of reactor antineutrino flux and spectrum dependence on the distance in the range 6-12 meters from the center of the reactor core. Using the measured spectrum and the distance dependence of antineutrino flux, we performed the model independent analysis of restrictions on the oscillation parameters $\Delta m^2_{14}$ and $\sin^2 2\theta_{14}$. The method of coherent addition of results of measurements is proposed. It allows us to directly observe the effect of oscillations. We observed the oscillation effect at CL $3.5\sigma$ in the vicinity of $\Delta m^2_{14} \approx 7.26\textrm{eV}^2$ and $\sin^2 2\theta_{14} \approx 0.38$. Combining the result of the Neutrino-4 experiment and the result of the gallium anomaly effect we obtained value $\sin^2 2\theta_{14} \approx 0.35 \pm 0.07 (5\sigma)$. The analysis of systematics effects is presented. Comparison with results of other experiments is presented. Future prospect of the experiment is discussed. It is necessary to notice that obtained values $\sin^2 2\theta_{14} \approx 0.35 \pm 0.07 (5\sigma)$ and $\Delta m^2_{14} \approx (7.3 \pm 0.7)\textrm{eV}^2$ allow make assessment on the mass of a neutrino: $m_{\beta} \approx 0.8\textrm{eV}$., Comment: 16 pages, 28 figures

The experiment "Neutrino-4" started in 2014 on a model, then it was continued on a full-scale detector, and now, has provided the measurement result on dependence of the flux and spectrum of reactor antineutrinos on the distance of 6 - 12 meters from the center of the reactor. One of the main problems is the correlated background from fast neutrons caused by space radiation. Attempts to suppress the background of fast neutrons by sectioning the detector have given some result. The relation of effect/background has improved up to 0.6. As a result, measurements of the difference in the counting rate of neutrino-like events (reactor ON - reactor OFF) have been obtained as dependence on distance from the reactor center. The fit of experimental dependence with the law $1/L^2$ give satisfactory result. The goodness of that fit is 81%. However, there was discovered experimental neutrino spectrum difference from calculated one. With achieved accuracy this difference does not change with distance. Therefore it cannot be interpreted as oscillations. Calculated spectrum form correction for experimental allow us to make proper analysis of oscillation parameters $\Delta m^2_{14}$ and $\sin^2(2\theta)$ limitations. Result of this analysis is exclusion of reactor and gallium anomalies area with 95% CL. Experiment future perspectives are discussed., Comment: 12 pages, 24 figures

This work is a survey on completely regular codes. Known properties, relations with other combinatorial structures and constructions are stated. The existence problem is also discussed and known results for some particular cases are established. In particular, we present a few new results on completely regular codes with covering radius 2 and on extended completely regular codes.

We construct new families of completely regular codes by concatenation methods. By combining parity check matrices of cyclic Hamming codes, we obtain families of completely regular codes. In all cases, we compute the intersection array of these codes. We also study when the extension of these codes gives completely regular codes. Some of these new codes are completely transitive.

In order to carry out research in the field of possible existence of a sterile neutrino the laboratory based on SM-3 reactor (Dimitrovgrad, Russia) was created to search for oscillations of reactor antineutrino. A moveable detector, protected with passive shielding from outer radiation, can be set at distance range 6 to 12 meters from the reactor core. Measurements of antineutrino flux at such short distances from the reactor core are carried out with moveable detector for the first time. The main difficulties of the measurements caused by cosmic background and it heavily decreases the precision of measurements. We present the analysis of measurements at small distances together with the data obtained in measurements at long distances in order to obtain parameters of sterile neutrino., Comment: 6 pages, 5 figures

In order to carry out research in the field of possible existence of a sterile neutrino the laboratory based on SM-3 reactor (Dimitrovgrad, Russia) was created to search for oscillations of reactor antineutrino. The prototype of a multi-section neutrino detector with liquid scintillator volume of 350 l was installed in the middle of 2015. It is a moveable inside the passive shielding detector, which can be set at distance range from 6 to 11 meters from the reactor core. Measurements of antineutrino flux at such short distances from the reactor core are carried out with moveable detector for the first time. The measurements with full-scale detector with liquid scintillator volume of 3 m^3 (5x10 sections) was started only in June, 2016. The today available data is presented in the article., Comment: 4 pages, 4 figures

In order to carry out research in the field of possible existence of sterile neutrino the laboratory based on SM-3 reactor (Dimitrovgrad, Russia) was created to search for oscillations of reactor antineutrino. The prototype of a multi-section neutrino detector with liquid scintillator volume of 350 l was installed in the middle of 2015. It is a moveable inside the passive shielding detector, which can be set at distance range from 6 to 11 meters from the reactor core. Measurements of antineutrino flux at such small distances from the reactor core carried out with movable detector for the first time. The measurements carried out with detector prototype demonstrated a possibility of measuring a reactor antineutrino flux in difficult conditions of cosmic background at Earth surface., Comment: 15 pages, 6 figures

A known Kronecker construction of completely regular codes has been investigated taking different alphabets in the component codes. This approach is also connected with lifting constructions of completely regular codes. We obtain several classes of completely regular codes with different parameters, but identical intersection array. Given a prime power $q$ and any two natural numbers $a,b$, we construct completely transitive codes over different fields with covering radius $\rho=\min\{a,b\}$ and identical intersection array, specifically, one code over $\F_{q^r}$ for each divisor $r$ of $a$ or $b$. As a corollary, for any prime power $q$, we show that distance regular bilinear forms graphs can be obtained as coset graphs from several completely regular codes with different parameters. Under the same conditions, an explicit construction of an infinite family of $q$-ary uniformly packed codes (in the wide sense) with covering radius $\rho$, which are not completely regular, is also given., Comment: Submitted to Journal of Combinatorial Theory, Series A

In connection with the question of possible existence of sterile neutrino the laboratory on the basis of SM-3 reactor was created to search for oscillations of reactor antineutrino. A prototype of a neutrino detector with scintillator volume of 400 l can be moved at the distance of 6-11 m from the reactor core. The measurements of background conditions have been made. It is shown that the main experimental problem is associated with cosmic radiation background. Test measurements of dependence of a reactor antineutrino flux on the distance from a reactor core have been made. The prospects of search for oscillations of reactor antineutrino at short distances are discussed., Comment: 24 pages, 23 figures

In this paper infinite families of linear binary nested completely regular codes are constructed. They have covering radius $\rho$ equal to $3$ or $4$, and are $1/2^i$-th parts, for $i\in\{1,\ldots,u\}$ of binary (respectively, extended binary) Hamming codes of length $n=2^m-1$ (respectively, $2^m$), where $m=2u$. In the usual way, i.e., as coset graphs, infinite families of embedded distance-regular coset graphs of diameter $D$ equal to $3$ or $4$ are constructed. In some cases, the constructed codes are also completely transitive codes and the corresponding coset graphs are distance-transitive.

One has investigated possibility of performing NEUTRINO-4 experiment on search for reactor neutrino oscillations into a sterile state at research reactors. The simulated experiment has been conducted at 16 MW reactor WWR-M in PNPI with the purpose of implementing a full scale experiment with the help of 100 MW reactor SM-3 in RIAR. Background conditions for making such an experiment have been examined at both reactors. The conclusion has been made on possible implementation of a full scale experiment NEUTRINO-4 at the reactor SM-3 in RIAR., Comment: 5 pages, 5 figures

In this paper new infinite families of linear binary completely transitive codes are presented. They have covering radius $\rho = 3$ and 4, and are a half part of the binary Hamming and the binary extended Hamming code of length $n=2^m-1$ and $2^m$, respectively, where $m$ is even. From these new completely transitive codes, in the usual way, i.e., as coset graphs, new presentations of infinite families of distance transitive coset graphs of diameter three and four, respectively, are constructed.

A new family of binary linear completely transitive (and, therefore, completely regular) codes is constructed. The covering radius of these codes is growing with the length of the code. In particular, for any integer r > 1, there exist two codes with d=3, covering radius r and length 2r(4r-1) and (2r+1)(4r+1), respectively. These new completely transitive codes induce, as coset graphs, a family of distance-transitive graphs of growing diameter., Comment: Submitted to Discrete mathematics. March 10, 2013

There has been designed an experimental project "Neutrino-4" for 100 MW reactor SM-3 to test the hypothesis of the "reactor antineutrino anomaly". Advantages of the reactor SM-3 for such an experiment are low background conditions as well as small dimensions of a reactor core - 35x42x42 cm3. One has carried on the Monte-Carlo modeling of a position sensitive antineutrino detector consisting of 5 operation sections, which as a result of displacement, covers the distance from 6 to 13 meters from the reactor core. One has succeeded in obtaining an experimental area of sensitivity to oscillation parameters, which enables to verify the hypothesis of reactor antineutrino oscillations into a sterile state., Comment: 13 pages, 10 figures

For any integer $\rho \geq 1$ and for any prime power q, the explicit construction of a infinite family of completely regular (and completely transitive) q-ary codes with d=3 and with covering radius $\rho$ is given. The intersection array is also computed. Under the same conditions, the explicit construction of an infinite family of q-ary uniformly packed codes (in the wide sense) with covering radius $\rho$, which are not completely regular, is also given. In both constructions the Kronecker product is the basic tool that has been used., Comment: Submitted to IT-IEEE. Theorem 1 in Section III was presented at the 2nd International Castle Meeting on Coding Theory and Applications (2ICMCTA), Medina del Campo, Spain, September 2008.}}