New extremal singly even self-dual codes of lengths 6464 and 6666

For lengths $64$ and $66$, we construct extremal singly even self-dual codes with weight enumerators for which no extremal singly even self-dual codes were previously known to exist. We also construct new $40$ inequivalent extremal doubly even self-dual $[64,32,12]$ codes with covering radius $12$ meeting the Delsarte bound.Comment: 13 pages. arXiv admin note: text overlap with arXiv:1706.0169

Self-dual codes with an automorphism of order 17

In this paper we study optimal binary self-dual codes with minimum distance 12 having an automorphism of order 17. We prove that all such codes have parameters [68 + f; 34 + f=2; 12]; f = 0; 2; 4 and automorphism of type 17- (4; f), f = 0; 2; 4 and provide a full classication of these codes. This classication gives: new values b = 17, 153, 170, 187, 221, 255 for = 0 in the weight enumerator W68,2 of [68, 34, 12] codes; new values b = 102, 136, 170, 204, 238, 272, 306, 340, 374, 408, 442, 476, 510, 544, 578, and 612 for g = 0 in W70,1 of [70, 35, 12] codes; numerous singly- and doubly-even [72, 36, 12] codes with new parameters in their weight enumerators

Classification of Binary Self-Dual [48,24,10] Codes with an Automorphism of Odd Prime Order

The purpose of this paper is to complete the classification of binary self-dual [48,24,10] codes with an automorphism of odd prime order. We prove that if there is a self-dual [48, 24, 10] code with an automorphism of type p-(c,f) with p being an odd prime, then p=3, c=16, f=0. By considering only an automorphism of type 3-(16,0), we prove that there are exactly 264 inequivalent self-dual [48, 24, 10] codes with an automorphism of odd prime order, equivalently, there are exactly 264 inequivalent cubic self-dual [48, 24, 10] codes.Comment: 11 pages, 4 table

A note on reducing the computation time for minimum distance and equivalence check of binary linear codes

In this paper we show the usability of the Gray code with constant weight words for computing linear combinations of codewords.This can lead to a big improvement of the computation time for finding the minimum distance of a code.We have also considered the usefulness of combinatorial 2-(t,k,1) designs when there are memory limitations to the number of objects (linear codes in particular) that can be tested for equivalence

INFLUENCE OF BASIC PARAMETERS OF THE LASER MARKING PROCESS ON STAINLESS STEEL SAMPLES

The role of basic quantities influencing the process of laser raster marking of AISI 304 stainless steel products using a fiber laser was investigated. Some dependencies were found when changing the contrast of the marking when changing the parameters in wide intervals. As the raster step increases, a non-linear decrease in contrast occurs as the rate of contrast decrease. Regarding the influence of the speed on the contrast, it was found that as the speed increases, the contrast of the marking decreases non-linearly, and as the step increases, the speed of the contrast decrease also increases. Above 20 kHz, the frequency has relatively little influence on the contrast, as with increasing frequency the contrast slowly increases and the dependence is almost linear. The effective energy is strongly influenced by the contrast. At effective energy values below 18 kJ/cm2 the contrast of the marking is insufficient for visual perception of a good quality marking, but in the interval from 6 kJ/cm2 to 46 kJ/cm2 the contrast increases very quickly. At values of the effective energy above 100 kJ/cm2, the contrast of the marking hardly changes. The obtained results can be used by the operators of laser systems to evaluate the working ranges and quickly determine the boundary areas of the optimal technological parameters when obtaining a good contrast in the laser marking of stainless steels with a fiber laser

On the ecological features of leaf ionome of some arboreal Rosaceae in Samara region conditions

Trees and shrubs of Rosaceae family possess a significant resource potential for the Samara region ecosystems. The quantitative study of elemental composition was carried out by X-ray fluorescence analysis (XRF) for leaves of 8 introduced and 3 native Rosaceae species. The features of five elements (K, Ca, Mn, Fe, Zn) levels are shown for them in comparison with the same parameters of two “reference plants” from different geographic locations. A very high Fe content and moderately high Mn and Zn contents were noted for leaves of all studied species. The detected high Ca concentration may be the result of plants development in soil environment with a naturally high Ca content. The revealed differences characterize the regional features of the leaf ionome, that reflecting the specifics of introduces plant species adaptation to new conditions and local species biogeochemical features