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1

Black-gray-white barcode based on error correction data encoding

Dychka Ivan, Sulema Olga

Journal of Applied Computer Science

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2019

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Vol. 27, nr 2

17--38

EN

The paper presents an approach based on using barcodes with three color gradations (white, gray, and black) instead of traditional black and white barcodes. Such three-color barcodes can be produced and read by using the same equipment as usual black and white barcodes, but due to the third color they have a higher information density. It is shown in the paper that in order to ensure high reliability and accuracy of barcoded information reading, it is necessary to encode the data with a Reed-Solomon correction code which is capable of correcting multiple errors. The method of data encoding and decoding in the Galois field GF(3m), where m is the degree of an irreducible polynomial, is proposed. The noise immunity of the black-gray-white barcode capable of multiple errors correction based on Reed-Solomon code is analyzed and discussed as well.

2

Havliček-Tietze configurations in various projective planes

Jakóbowski J., Kacperek D.

Demonstratio Mathematica

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2014

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Vol. 47, nr 4

979--988

EN

A. Lewandowski and H. Makowiecka proved in 1979 that existence of the Havliček–Tietze configuration (shortly H - T) in the desarguesian projective plane is equivalent to existence in the associated field, a root of polynomial x2 + x + 1, different from 1. We show that such a configuration exists in every projective plane over Galois field GF(p2) for p ≠ 3. As it has been demonstrated, in a projective plane over arbitrary field F, each hexagon contained in H - T, satisfies the Pappus–Pascal axiom, even if F is noncommutative. Moreover, such a hexagon either is pascalian or has exactly one pair of opposite sides intersecting at a point collinear with two points not belonging to these sides. In particular, all such hexagons are pascalian iff char F = 2. For the (noncommutative) field of quaternions, we have determined the set of all roots of the mentioned polynomial. Every H - T is the special Pappus configuration, in which three main diagonals of the hexagon are concurrent.

3

Implementacja sprzętowa wybranych elementów gcm-aes w układzie programowalnym na karcie netfpga

Romaszkan W., Kasperek J., Rajda P., Pacyna P., Konorski J.

Zeszyty Naukowe Wydziału ETI Politechniki Gdańskiej. Technologie Informacyjne

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2013

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T. 21

7--19

PL

Artykuł przedstawia projekt oraz implementację modułu realizującego mnożenie w skończonym polu Galois GF(2128), przeznaczonego do pracy w szyfratorze AES-GCM. Moduł został zrealizowany w taki sposób, aby umożliwić jego implementację w układach programowalnych FPGA na kartach NetFPGA1G oraz NetFPGA10G. Uwaga skupiła się na zapewnieniu należytej minimalnej częstotliwości taktowania zegara oraz odpowiedniej szybkości przetwarzania danych, przy uwzględnieniu ograniczonych zasobów układów programowalnych.

EN

The paper reports on the design and implementation of a Galois GF(2128) multiplier for use in AES-GCM encryption module. The GF(2128) multiplier has been designed to satisfy the requirements and constraints of FPGA circuits on NetFPGA1G and NetFPGA10G development boards.

4

Modeling and the processes analysis in engineering ecology

Brakovich A., Kolesnikov V., Romantsevich A., Urbanovich P., Zharsky I.

Przegląd Elektrotechniczny

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2008

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R. 84, nr 3

155-157

EN

The method of information networks construction with the decision of a problem of orthogonal tables packing is presented. This model is realized by multiplication and addition of Galois fields elements in a ring of classes of deductions on module according to coordinates of top gathered planes on infinity.

PL

Opracowano metodę budowy sieci informacyjnych z wykorzystaniem problemu pakowania ortogonalnych tablic poprzez mnożenie i dodawanie elementów pola Galois'a w pierścieniu klas modulo zgodnie ze współrzędnymi wierzchołków leżących na płaszczyźnie w nieskończoności.